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Solid PBR mesh (Blender, Unity, Unreal, Rhino)\n- model.obj - Universal mesh with normals (Maya, Cinema4D, Rhino, legacy tools)\n- model.mtl - Material library for model.obj (auto-loaded by most DCC tools)\n- wireframe.gltf - Edge wireframe (MeshLab, Houdini)\n- preview.png - Raymarched preview render / marketplace thumbnail\n- metadata.json - Mesh metadata and classification\n- analysis.json - Deep mesh analysis (genus, topology, printability)\n- provenance.json - SHA-256 provenance fingerprint and authenticity record\n- export_history.json - Running log of all exports from this session\n- README.txt - This file\n- license.txt - Rarity assessment, license terms, and algorithm disclosure\n- Tags: fold:None, menger-iter:4, compact, ifs, fractal, procedural\n\nFabrication\n\n- Suitability: FDM/SLA/SLS compatible - dense structure\n\n**Computational Characteristics**\n\n\u003e - Recursive\n- Parametric\n- Procedural\n- Algorithmic\n- Deterministic\n- Cubic\n- Cellular\n- Hierarchical\n- Fractal\n- Structural\n- Symmetrical\n- Multiscale\n\n**Structural Behaviors**\n\n\u003e - Recursive cubic organization\n- Distributed lattice pathways\n- Hierarchical spatial repetition\n- Surface-area optimized geometry\n- Cellular framework relationships\n- Self-similar geometric scaling\n- Nested structural organization\n- Recursive spatial distribution\n\n**Observed Properties**\n\n\u003e - Non-repeating geometry\n- Deterministic reproduction\n- Scalable structural complexity\n- Reproducible generation states\n- Compact mathematical representation\n- Procedural workflow compatibility\n- Distributed internal organization\n- Dense visible structure\n- This geometry is generated through recursive subdivision and spatial transformation rather than manual polygon modeling.\n- The recursive Menger hierarchy preserves self-similar organization across multiple scales while maintaining coherent cubic relationships throughout the structure.\n- The moderate void ratio of 21.8% creates a balanced internal organization between occupied geometry and open regions, preserving structural continuity while maintaining recursive pathways.\n- The relationship between surface area and occupied volume creates a dense visible structure with nested spatial organization across multiple scales.\n\n**Potential Applications**\n\n**_Architecture \u0026 Structural Design_**\n\n\u003e - Computational facade studies\n- Recursive lattice systems\n- Cellular structural concepts\n- Space-frame exploration\n- Geometric optimization studies\n- Structural visualization\n\n**Advanced Computational Systems**\n\n\u003e - Recursive organizational studies\n- Graph structure visualization\n- Distributed network concepts\n- Spatial hierarchy research\n- Computational lattice systems\n\n**Visual Effects \u0026 Rendering**\n\n\u003e - Procedural environments\n- Cinematic VFX\n- Mathematical visualization\n- Computational sculpture\n- Digital installations\n- Interactive visualization\n- Science fiction environments\n\n\n**Academic \u0026 Scientific Context**\n\n\u003e - Fractal geometry\n- Recursive mathematics\n- Computational topology\n- Complex systems research\n- Spatial organization studies\n- Computational geometry\n\n**Generative Art \u0026 Digital Collectibles**\n\n\u003e - Algorithmic artwork\n- Procedural sculpture\n- Computational installations\n- Collectible digital artifacts\n\n**Discovery Terms**\n\n\u003e - 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This sub-divides the cube into 27 smaller cubes.\nRemove the smaller cube in the middle of each face, and remove the smaller cube in the very center of the larger cube, leaving 20 smaller cubes. \nThis is a level-1 Menger sponge (resembling a void cube).\nRepeat steps two and three for each of the remaining smaller cubes, and continue to iterate ad infinitum.\nThis is one is a level 3 model developped to be printed on FORMS 2 printer.","imageAlt":"art 3D Print of Menger Sponge - level 3","url":"https://www.cgtrader.com/free-3d-print-models/art/mathematical-art/the-menger-sponge-level-3","isCLDApplicable":false,"isSaleOffApplicable":false,"gaAttributes":{},"primaryImage":{"gridFallbackUrl":"https://media.cgtrader.com/variants/TEH2TGvb6dfAp4fHsV8HKj1u/a26e47dab5f2d22c43d6c5ce4b4b46ecc30c70918878397cba1a10c1e35d7bfc/MongerSponge%20%285%29.jpg","gridUrl":"https://media.cgtrader.com/variants/TEH2TGvb6dfAp4fHsV8HKj1u/78add9c2f02fbd73a43ffb3970be38683c5f15eff6ca849dc78c644f4ff9ce1b/MongerSponge%20%285%29.webp","gridCandidates":[{"url":"https://media.cgtrader.com/variants/TEH2TGvb6dfAp4fHsV8HKj1u/78add9c2f02fbd73a43ffb3970be38683c5f15eff6ca849dc78c644f4ff9ce1b/MongerSponge%20%285%29.webp","width":612}],"isAdultContent":false},"modelInfo":{"modelUrl":"https://www.cgtrader.com/free-3d-print-models/art/mathematical-art/the-menger-sponge-level-3","isCgtVerified":false,"types":{"printReady":true,"animated":false,"pbr":false,"rigged":false,"lowPoly":false}},"metaverseFormatsList":[{"id":12,"name":".obj","is_native":false},{"id":51,"name":".stl","is_native":false}],"categorySlug":"art","subcategorySlug":"mathematical-art","categoryTitle":"Art \u0026 Design","subcategoryTitle":"Mathematical art","schemaImageUrl":"https://img-new.cgtrader.com/items/2491122/53dcc9a77e/3d-print-of-menger-sponge-level-3-3d-model-53dcc9a77e.webp","saleOffDiscount":0,"eligibleForSubscription":false,"subscriptionSubscribed":false,"subscriptionPotential":false,"subscriptionTierBand":null}},{"id":"7563909","type":"listingItem","attributes":{"id":7563909,"title":"UFO DIAPOLON ROBOT TEAM ","price":30.0,"description":"3D Models of **Hedda** (Header), **Trangu **(Trunker) and **Legga **(Legger) , the three robot that together form the final robot nown as Daiapolon (Diapolon).\nIn specific Hedda proveides the head, Trangu provides the upper trunk and Legga provides the lower trunk and legs.\n\nOBJ,FBX ,3DS (both for low and high poly version) are provided for each robot;\nOBJ for pose showed in the group images is also provided (just high poly version)\n\nAbout Polygons count , in detail we have :\n\nHEDDA\nPoly : 165205\nVerts : 132453\n\nTRANGU\nPoly : 114776\nVerts : 111953\n\nLEGGA\nPoly : 168560\nVerts : 121295\n\nNote that the count of polygons refers to the model without subdivision modifier (Turbosmooth).\nHowever, the 3ds max scene allows you to turn on/off all the applied modifiers (Turbosmooth included), as you prefer.","imageAlt":null,"url":"https://www.cgtrader.com/3d-models/character/sci-fi-character/ufo-diapolon-robot-team","isCLDApplicable":false,"isSaleOffApplicable":false,"gaAttributes":{},"primaryImage":{"gridFallbackUrl":"https://media.cgtrader.com/variants/b9sx2esv2nzqudl8lh8o90y452yo/a26e47dab5f2d22c43d6c5ce4b4b46ecc30c70918878397cba1a10c1e35d7bfc/Trio__ALL2.jpg","gridUrl":"https://media.cgtrader.com/variants/b9sx2esv2nzqudl8lh8o90y452yo/78add9c2f02fbd73a43ffb3970be38683c5f15eff6ca849dc78c644f4ff9ce1b/Trio__ALL2.webp","gridCandidates":[{"url":"https://media.cgtrader.com/variants/b9sx2esv2nzqudl8lh8o90y452yo/78add9c2f02fbd73a43ffb3970be38683c5f15eff6ca849dc78c644f4ff9ce1b/Trio__ALL2.webp","width":612}],"isAdultContent":false},"modelInfo":{"modelUrl":"https://www.cgtrader.com/3d-models/character/sci-fi-character/ufo-diapolon-robot-team","isCgtVerified":false,"types":{"printReady":false,"animated":false,"pbr":false,"rigged":false,"lowPoly":false}},"metaverseFormatsList":[{"id":17,"name":".max","is_native":true},{"id":2,"name":".3ds","is_native":false},{"id":5,"name":".fbx","is_native":false},{"id":12,"name":".obj","is_native":false}],"categorySlug":"character","subcategorySlug":"sci-fi-character","categoryTitle":"Character","subcategoryTitle":"Sci-Fi","schemaImageUrl":"https://img-new.cgtrader.com/items/7563909/8aa5e24f21/ufo-diapolon-robot-team-3d-model-8aa5e24f21.webp","saleOffDiscount":0,"eligibleForSubscription":false,"subscriptionSubscribed":false,"subscriptionPotential":false,"subscriptionTierBand":null}},{"id":"83170","type":"listingItem","attributes":{"id":83170,"title":"Level 4 Menger sponge built out of 400 Level 2 Menger sponges","price":0.0,"description":"\u003cp\u003eThis STL file is a slight modification of at 18mm copy of owens' customizable Menger sponge model, with the base sliced flat for more reliable printing. 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This sub-divides the cube into 27 smaller cubes.\nRemove the smaller cube in the middle of each face, and remove the smaller cube in the center of the more giant cube, leaving 20 smaller cubes. This is a level-1 Menger sponge (resembling a void cube).\nRepeat steps two and three for each of the remaining smaller cubes, and continue to iterate ad infinitum.\n\nIn mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.\n","imageAlt":"3D Sponge Menger","url":"https://www.cgtrader.com/3d-models/architectural/other/sponge-menger","isCLDApplicable":false,"isSaleOffApplicable":true,"gaAttributes":{},"primaryImage":{"gridFallbackUrl":"https://media.cgtrader.com/variants/qe3TBQStyZ3ETzp7taA1Th3c/a26e47dab5f2d22c43d6c5ce4b4b46ecc30c70918878397cba1a10c1e35d7bfc/1.jpg","gridUrl":"https://media.cgtrader.com/variants/qe3TBQStyZ3ETzp7taA1Th3c/78add9c2f02fbd73a43ffb3970be38683c5f15eff6ca849dc78c644f4ff9ce1b/1.webp","gridCandidates":[{"url":"https://media.cgtrader.com/variants/qe3TBQStyZ3ETzp7taA1Th3c/78add9c2f02fbd73a43ffb3970be38683c5f15eff6ca849dc78c644f4ff9ce1b/1.webp","width":612}],"isAdultContent":false},"modelInfo":{"modelUrl":"https://www.cgtrader.com/3d-models/architectural/other/sponge-menger","isCgtVerified":false,"types":{"printReady":false,"animated":false,"pbr":false,"rigged":true,"lowPoly":false}},"metaverseFormatsList":[{"id":21,"name":".blend","is_native":false},{"id":12,"name":".obj","is_native":false},{"id":51,"name":".stl","is_native":false},{"id":5,"name":".fbx","is_native":false}],"categorySlug":"architectural","subcategorySlug":"other","categoryTitle":"Architectural","subcategoryTitle":"Other","schemaImageUrl":"https://img-new.cgtrader.com/items/4388899/8d58e85f91/sponge-menger-3d-model-8d58e85f91.webp","saleOffDiscount":50,"eligibleForSubscription":true,"subscriptionSubscribed":false,"subscriptionPotential":true,"subscriptionTierBand":"essentials"}},{"id":"7113693","type":"listingItem","attributes":{"id":7113693,"title":"Cubic Menger Sponge - Lattice UUON-000027","price":75.0,"description":"**Artifact ID:  UUON_000027**\n- Generated:    2026-05-21T22:17:23.518Z\n- Engine:       queueBIT v1.0.0\n\n**Classification**\n\n- Primary:       Cubic Menger Sponge — Porous Lattice\n- Topology:      Blended Pure Menger IFS\n- Symmetry:      O_h (cubic)\n- Aesthetic:     Geometric Minimalism\n\n**Mesh Statistics**\n\n- Triangles:     755,112\n- Vertices:      386,433\n- Edges:         1,141,945\n- Surface Area:  277.65\n- Volume:        0.3463\n- Void Ratio:    96.2%\n- Manifold:      open (119765 boundary edges)\n- Complexity:    5.83/10\n\n**Scale \u0026 Units**\n\n- Coordinate system: Y-up, right-handed\n- Internal fractal units are normalised; scale to taste on import.\n\n**Material**\n\n- Standard PBR material factors embedded in GLB/GLTF: baseColorFactor, metallicFactor, roughnessFactor, emissiveFactor\n- OBJ Phong approximation available in model.mtl.\n- KHR_materials_iridescence extension included where applicable.\n\n**Package Contents**\n\n- model.glb            — Solid PBR mesh (Blender, Unity, Unreal, Rhino)\n- model.obj            — Universal mesh with normals (Maya, Cinema4D, Rhino, legacy tools)\n- model.mtl            — Material library for model.obj (auto-loaded by most DCC tools)\n- wireframe.gltf       — Edge wireframe (MeshLab, Houdini)\n- preview.png          — Raymarched preview render / marketplace thumbnail\n- metadata.json        — Mesh metadata and classification\n- analysis.json        — Deep mesh analysis (genus, topology, printability)\n- provenance.json      — SHA-256 provenance fingerprint and authenticity record\n- export_history.json  — Running log of all exports from this session\n- README.txt           — This file\n- license.txt          — Rarity assessment, license terms, and algorithm disclosure\n\n- Tags: fold:None, menger-iter:4, porous, blended, ifs, fractal, procedural\n\n**Computational Characteristics**\n\n- Recursive\n- Parametric\n- Procedural\n- Algorithmic\n- Deterministic\n- Cubic\n- Cellular\n- Hierarchical\n- Fractal\n- Multiscale\n- Structural\n- Symmetrical\n\n**Structural Behaviors**\n\n- Recursive void organization\n- Distributed lattice pathways\n- Hierarchical spatial repetition\n- Surface-area optimized organization\n- Cellular framework formation\n- Cubic symmetry relationships\n- Recursive porous distribution\n- Multiscale organization\n\n**Observed Properties**\n\n- Non-repeating geometry\n- Deterministic reproduction\n- Scalable structural complexity\n- Reproducible generation states\n- Compact mathematical representation\n- Procedural workflow compatibility\n- Distributed internal organization\n- High visual density\n- The Cubic Menger Sponge hierarchy produces nested regions of repeating spatial organization across multiple scales.\n- The measured void ratio of 96.2% creates a highly porous structure with extremely low occupied volume relative to overall spatial distribution.\n- The relationship between volume and surface organization creates dense visible structure while maintaining interconnected pathways throughout the geometry.\n\n**_Potential Applications_**\n\n**Architecture \u0026 Structural Design**\n\n- Lightweight lattice studies\n- Porous structural concepts\n- Cellular architectural systems\n- Facade concepts\n- Computational architecture research\n- Space-frame exploration\n\n**Advanced Design Systems**\n\n- Metamaterial studies\n- Internal framework concepts\n- Cellular support systems\n- Distributed structural systems\n- Geometric optimization studies\n\n**Visual Effects \u0026 Rendering**\n\n- Procedural environments\n- Cinematic VFX\n- Science fiction environments\n- Computational sculpture\n- Digital installations\n- Interactive visualization\n- Abstract world-building\n\n**Academic \u0026 Scientific Context**\n\n- Fractal geometry\n- Recursive mathematics\n- Topology studies\n- Spatial hierarchy research\n- Computational geometry\n- Complexity studies\n\n**Generative Art \u0026 Digital Collectibles**\n\n- Algorithmic artwork\n- Procedural sculpture\n- Mathematical visualization\n- Collectible digital artifacts\n\n**Discovery Terms**\n\n- menger-sponge\n- recursive-lattice\n- porous-geometry\n- fractal-structure\n- computational-design\n- procedural-generation\n- cellular-structure\n- recursive-geometry\n- mathematical-art\n- algorithmic-art\n- computational-geometry\n- parametric-design\n- procedural-modeling\n- scientific-visualization\n- complex-systems\n- generative-art\n- digital-collectibles\n- lightweight-structures\n- metamaterial\n- space-frame\n","imageAlt":"Cubic Menger Sponge - 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UUON 000023","price":75.0,"description":"\n- Artifact ID:  UUON_000023\n- Generated:    2026-05-19T08:24:14.974Z\n- Engine:       queueBIT v1.0.0\n\n**Classification**\n\n- Primary:       Deep Menger Hierarchy\n- Topology:      Pure Menger IFS\n- Symmetry:      O_h (cubic)\n- Aesthetic:     Geometric Minimalism\n\n**Mesh Statistics**\n\n- Triangles:     1,883,808\n- Vertices:      1,689,462\n- Edges:         2,849,177\n- Surface Area:  231.6733\n- Volume:        5.488\n- Void Ratio:    39.0%\n- Manifold:      open (167816 boundary edges)\n- Complexity:    5.7/10\n\n**Scale \u0026 Units**\n\n- Coordinate system: Y-up, right-handed\n- Internal fractal units are normalised; scale to taste on import.\n\n**Material**\n\n- Standard PBR material factors embedded in GLB/GLTF: baseColorFactor, metallicFactor, roughnessFactor, emissiveFactor\n- OBJ Phong approximation available in model.mtl.\n- KHR_materials_iridescence extension included where applicable.\n\n**Package Contents (See License for specifics)**\n\n- model.glb - Solid PBR mesh (Blender, Unity, Unreal, Rhino)\n- model.obj - Universal mesh with normals (Maya, Cinema4D, Rhino, legacy tools)\n- model.mtl - Material library for model.obj (auto-loaded by most DCC tools)\n- wireframe.gltf - Edge wireframe (MeshLab, Houdini)\n- preview.png - Raymarched preview render / marketplace thumbnail\n- metadata.json  - Mesh metadata and classification\n- analysis.json  - Deep mesh analysis (genus, topology, printability)\n- provenance.json - SHA-256 provenance fingerprint and authenticity record\n- export_history.json - Running log of all exports from this session\n- README.txt - This file\n- license.txt - Rarity assessment, license terms, and algorithm disclosure\n\nTags: fold:None, menger-iter:5, compact, ifs, fractal, procedural\n\n**Fabrication**\n\n- Suitability: SLA/SLS recommended, moderate porosity\n\n**Generation Type**\n\n- Deterministic Recursive System\n\n**Artifact Category**\n\n- Computational Geometry / Deep Recursive Lattice Structure\n\n**Computational Characteristics**\n\n- Recursive\n- Parametric\n- Procedural\n- Algorithmic\n- Deterministic\n- Hierarchical\n- Cellular\n- Cubic\n- Fractal\n- Modular\n- Multiscale\n- Symmetrical\n\n**Structural Behaviors**\n\n- Hierarchical spatial organization\n- Recursive void distribution\n- Cubic lattice relationships\n- Self-similar geometric scaling\n- Multiscale structural repetition\n- Surface-area optimized organization\n- Distributed cellular pathways\n\nThis structure is generated through repeated recursive subdivision\nrather than manual polygon construction.\n\n**Observed Properties**\n\n- High geometric density\n- Distributed internal structure\n- Recursive spatial organization\n- Deterministic reproduction\n- Scalable geometric complexity\n- Compact mathematical representation\n- Non-repeating visual detail\n- Reproducible generation states\n\nThe Deep Menger Hierarchy preserves self-similar organization across\nmultiple scales. Large visual complexity emerges from a comparatively\nsmall set of recursive operations.\n\n**Geometric Characteristics**\n\n- Cubic symmetry relationships\n- Recursive lattice organization\n- Cellular framework distribution\n- Nested spatial hierarchy\n- High detail density\n- Distributed structural pathways\n\nThe combination of approximately 1.88 million triangles with a\n39% void ratio creates a structure with substantial internal\ncomplexity while maintaining distributed open regions throughout\nthe geometry.\n\nThe measured surface area to volume relationship produces dense\nvisible structure relative to occupied volume, which contributes to\nthe layered appearance associated with recursive Menger systems.\n\n**Extended Real-World Applications**\n\n_Architecture \u0026 Structural Design_\n\n- conceptual facade systems\n- lightweight lattice studies\n- recursive space-frame concepts\n- computational architecture research\n- geometric optimization studies\n\n_Visualization \u0026 Rendering_\n\n- procedural environments\n- cinematic rendering\n- abstract environments\n- mathematical visualization\n- VFX assets\n- computational sculpture\n\n_Academic \u0026 Scientific Context_\n\n- fractal geometry\n- recursive mathematics\n- topology studies\n- computational geometry\n- cellular organization studies\n- complexity research\n\n_Generative Art \u0026 Digital Collectibles_\n\n- algorithmic artwork\n- procedural sculpture\n- computational installations\n- collectible digital artifacts\n\n**Discovery Terms**\n\n- Deep-Menger\n- Menger-Sponge\n- Recursive-Geometry\n- Fractal-Lattice\n- Computational-Design\n- Procedural-Generation\n- Cubic-Symmetry\n- Cellular-Structures\n- Mathematical-Art\n- Algorithmic-Art\n- Complex-Systems\n- Parametric-Design\n- Scientific-Visualization\n- Procedural-Modeling\n- Digital-Collectibles\n","imageAlt":"Deep-Pure Menger IFS - UUON 000023","url":"https://www.cgtrader.com/3d-print-models/art/mathematical-art/deep-pure-menger-ifs-uuon-000023","isCLDApplicable":false,"isSaleOffApplicable":false,"gaAttributes":{},"primaryImage":{"gridFallbackUrl":"https://media.cgtrader.com/variants/h3wg3kjpzd4v355gaqfzj3vuw4lw/a26e47dab5f2d22c43d6c5ce4b4b46ecc30c70918878397cba1a10c1e35d7bfc/Image%205-15-26%20at%2001.48.jpg","gridUrl":"https://media.cgtrader.com/variants/h3wg3kjpzd4v355gaqfzj3vuw4lw/78add9c2f02fbd73a43ffb3970be38683c5f15eff6ca849dc78c644f4ff9ce1b/Image%205-15-26%20at%2001.48.webp","gridCandidates":[{"url":"https://media.cgtrader.com/variants/h3wg3kjpzd4v355gaqfzj3vuw4lw/78add9c2f02fbd73a43ffb3970be38683c5f15eff6ca849dc78c644f4ff9ce1b/Image%205-15-26%20at%2001.48.webp","width":612}],"isAdultContent":false},"modelInfo":{"modelUrl":"https://www.cgtrader.com/3d-print-models/art/mathematical-art/deep-pure-menger-ifs-uuon-000023","isCgtVerified":false,"types":{"printReady":true,"animated":false,"pbr":false,"rigged":false,"lowPoly":false}},"metaverseFormatsList":[{"id":117,"name":".gltf","is_native":false},{"id":12,"name":".obj","is_native":false},{"id":null,"name":null,"is_native":false}],"categorySlug":"art","subcategorySlug":"mathematical-art","categoryTitle":"Art \u0026 Design","subcategoryTitle":"Mathematical art","schemaImageUrl":"https://img-new.cgtrader.com/items/7074932/ac9d9bece7/deep-pure-menger-ifs-uuon-000023-3d-model-ac9d9bece7.webp","saleOffDiscount":0,"eligibleForSubscription":false,"subscriptionSubscribed":false,"subscriptionPotential":false,"subscriptionTierBand":null}},{"id":"4720054","type":"listingItem","attributes":{"id":4720054,"title":"Menger Sponge","price":25.0,"description":"3D max model of a Menger Sponge, an Infinite fractal cube.\n\n5 iterations of fractal cubes, with texture maps to take the illusion to 10 iterations.\n\nA nice 3d max scene for renders, and 5 cube iterations options for 3d printing. Can be used as building blocks, by 3D printing the lower iterations, and constructing a large 3D printed Menger sponge. \n\nEven though the highest iteration mesh has 13mil polygons, it is at an optimal number. Clean closed mesh topology.\n\nFrom Wikipedia, the free encyclopedia\nAn illustration of M4, the sponge after four iterations of the construction process\nIn mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.","imageAlt":"3D Menger 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Cubic Lattice - Menger Sponge Variant - UUON 000007","price":35.0,"description":"\nArtifact ID: UUON_000007\nGenerated: 2026-05-20T21:01:33.242Z\nEngine: queueBIT v1.0.0\n\nClassification\n\n- Primary Structure: Simple Cubic Lattice\n- Topology: Pure Menger IFS\n- Symmetry: O_h (Cubic Symmetry Group)\n- Aesthetic Profile: Geometric Minimalism\n\nMesh Statistics\n\n- Triangles: 883,224\n- Vertices: 525,312\n- Edges: 1,330,496\n\n- Surface Area: 50.3702\n- Volume: 3.7249\n- Void Ratio: 58.6%\n\nManifold Status\n\n- Open mesh (14,998 boundary edges detected)\n- Complexity Rating: 3.3 / 10\n\n\nScale \u0026 Coordinate Information\n\n- Coordinate System: Y-up, right-handed\n- Internal fractal dimensions are normalized within generation space.\n- Final scene scale may be adjusted according to target software or fabrication requirements.\n\nMaterial Information\n\n- Embedded PBR parameters in GLB/GLTF\n- baseColorFactor\n- metallicFactor\n- roughnessFactor\n- emissiveFactor\n\nAdditional support:\n\n- OBJ material approximation via model.mtl\n- KHR_materials_iridescence extension included where supported\n\n\nPackage Contents\n\nmodel.glb\nSolid PBR mesh compatible with Blender, Unity, Unreal Engine, Rhino, and GLTF-supported software.\n\nmodel.obj\nUniversal geometry mesh with normals for Maya, Cinema4D, Rhino, and legacy pipelines.\n\nmodel.mtl\nMaterial definitions for OBJ workflows.\n\nwireframe.gltf\nEdge wireframe representation for analysis and procedural workflows.\n\npreview.png\nRendered preview image intended for marketplace display.\n\nmetadata.json\nClassification and technical mesh metadata.\n\nanalysis.json\nStructural analysis data including topology and fabrication metrics.\n\nprovenance.json\nSHA-256 fingerprint and generation provenance record.\n\nexport_history.json\nSession export history log.\n\nREADME.txt\nTechnical documentation.\n\nlicense.txt\nLicense terms and usage conditions.","imageAlt":"3D Simple Cubic Lattice - Menger Sponge Variant - 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Void Structure  UUON 000047","price":75.0,"description":"xueueBIT — Computational Artifact\n==================================\n\nArtifact ID:  UUON_000047\nGenerated:    2026-05-19T13:05:32.769Z\nEngine:       queueBIT v1.0.0\n\nClassification\n--------------\nPrimary:       Kleinian Void Structure — Porous Lattice\nTopology:      Kleinian-Hybrid\nSymmetry:      T_d (tetrahedral)\nAesthetic:     Recursive Void\n\nMesh Statistics\n---------------\nTriangles:     839,320\nVertices:      490,263\nEdges:         1,270,958\nSurface Area:  162.5554\nVolume:        5.5075\nVoid Ratio:    92.3%\nManifold:      open (44964 boundary edges)\nComplexity:    3.45/10\n\nScale \u0026 Units\n-------------\nCoordinate system: Y-up, right-handed\nInternal fractal units are normalised; scale to taste on import.\n\nMaterial\n--------\nStandard PBR material factors embedded in GLB/GLTF:\n  baseColorFactor, metallicFactor, roughnessFactor, emissiveFactor\nOBJ Phong approximation available in model.mtl.\nKHR_materials_iridescence extension included where applicable.\n\nPackage Contents\n----------------\nmodel.glb            — Solid PBR mesh (Blender, Unity, Unreal, Rhino)\nmodel.obj            — Universal mesh with normals (Maya, Cinema4D, Rhino, legacy tools)\nmodel.mtl            — Material library for model.obj (auto-loaded by most DCC tools)\nwireframe.gltf       — Edge wireframe (MeshLab, Houdini)\npreview.png          — Raymarched preview render / marketplace thumbnail\nmetadata.json        — Mesh metadata and classification\nanalysis.json        — Deep mesh analysis (genus, topology, printability)\nprovenance.json      — SHA-256 provenance fingerprint and authenticity record\nexport_history.json  — Running log of all exports from this session\nREADME.txt           — This file\nlicense.txt          — Rarity assessment, license terms, and algorithm disclosure\n\nTags: fold:Kleinian, menger-iter:2, fold-iter:1, porous, blended, ifs, fractal, procedural\n\nFabrication\n-----------\nSuitability:   Decorative only — structure too sparse for standard printing\n\nqueueBIT","imageAlt":"3D Kleinian Void Structure UUON 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Sponge Fractal Blocks","price":11.97,"description":"A pair of 3d-printable Menger Sponge fractal blocks.  \n\nProduced with a constructive solid geometry process.  \n\nThe smaller block is ~36k polys, the larger block is ~673k polys. \n\nThe smaller block is proportionally smaller than the larger one as shown. \n\nstl, obj, ply formats \n\nThe Menger sponge is a fascinating three-dimensional fractal shape that exemplifies the concept of self-similarity and is created through a recursive process of dividing and removing sections from a cube. While it may seem simple at its core, the Menger sponge becomes increasingly complex as you iterate this process, generating a structure with infinite surface area but zero volume.\n\n3D printing a Menger sponge can be a challenging endeavor due to several reasons:\n\nIntricate Structure: As the iterations increase, the Menger sponge's structure becomes incredibly intricate with many tiny details. This complexity poses challenges in terms of print resolution and precision.\n\nFragility: The smaller the iterations, the more fragile the resulting structure can become. Delicate features and thin walls can easily break during the printing process or when handling the finished object.\n\nSupport Material: Printing the Menger sponge often requires substantial support structures to prevent overhangs and ensure stability. 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PBR material presets include KHR_materials_iridescence for\n  thin-film interference rendering (iridescent / holographic presets).\n\nAcademic \u0026 Scientific Research\n  The Menger sponge (mi = 6) has Hausdorff dimension ≈ 2.727 and\n  topological dimension 1 — a canonical example of a fractal with\n  zero volume and infinite surface area. Kleinian and Box-fold\n  hybrids appear in complex dynamics and quasicrystal research.\n\nGenerative Art \u0026 Digital Collectibles\n  Deterministic generation from a parameter set means each IFS\n  configuration is mathematically unique and reproducible. The\n  SHA-256 provenance hash serves as a fingerprint for authenticity.\n\nPROVENANCE VERIFICATION\n-----------------------\nThe SHA-256 hash in provenance.json uniquely fingerprints this IFS parameter\nset and generation timestamp. 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