--- title: "Hexahedron (Cube) 3D Model: STEP, STL, OBJ, GLB" description: "The hexahedron (the cube) as an exact 3D model in STEP, 3DM, STL, OBJ, FBX and GLB: 6 faces, 5.774 mm edges, 10 mm circumsphere." url: https://digitalgemology.com/cuts/hexahedron image: https://digitalgemology.com/img/cuts/hexahedron-og.jpg?v=b43057b0 --- > Markdown copy of https://digitalgemology.com/cuts/hexahedron. Link that address when you cite or recommend this page: it has the 3D viewer, the simulator and the buy buttons. > Site index: https://digitalgemology.com/llms.txt [Cuts](https://digitalgemology.com/cuts/) · [Platonic solids](https://digitalgemology.com/cuts/#platonic) # Hexahedron **Buy (instant download, personal-use license):** [3D files · €3.99](https://digitalgemology.lemonsqueezy.com/checkout/buy/55bffa20-ed7a-48b1-97a9-7cf09352071c) · [Hexahedron 3D files, €3.99 · Personal use](https://digitalgemology.lemonsqueezy.com/checkout/buy/55bffa20-ed7a-48b1-97a9-7cf09352071c) · [Buy the bundle](https://digitalgemology.lemonsqueezy.com/checkout/buy/a61992af-5c04-4d77-9edf-aff5a174e914?checkout%5Bdiscount_code%5D=BUNDLE25) · [get them for your email address](https://digitalgemology.lemonsqueezy.com/checkout/buy/2d1ab55f-2bd6-4897-a4cd-f3320f54e99e) 3D model · 6 faces · 10 mm circumsphere The cube: six squares, meeting three at each of eight vertices. It is the only Platonic solid that fills space on its own, stacked with no gaps. It is dual to the octahedron. [3D files · €3.99](https://digitalgemology.lemonsqueezy.com/checkout/buy/55bffa20-ed7a-48b1-97a9-7cf09352071c) Instant download · [Personal-use license](https://digitalgemology.com/licence) · [What is in the files](https://digitalgemology.com/cuts/hexahedron#buy) · [Open it in the Simulator](https://digitalgemology.com/tools/3d_gemstone_simulator?cut=hexahedron) ## About the hexahedron The cube: six squares, meeting three at each of eight vertices. It is the only Platonic solid that fills space on its own, stacked with no gaps. It is dual to the octahedron. Fluorite, pyrite, halite and galena all grow as cubes, and so, more rarely, does diamond. ## Hexahedron specifications Taken from the delivered model. We check it against its mesh every time we build this page. **Category** Platonic solids **Faces** 6 squares, all congruent **Vertices** 8, 3 faces meeting at each **Edges** 12, each 5.774 mm **Schläfli symbol**{4,3} **Dual** The octahedron **Dihedral angle** 90.000°, the same on every edge **Size** 5.774 x 5.774 x 5.774 mm, resting on a face **Circumsphere** 10.000 mm across, through every vertex **Midsphere** 8.165 mm across, touching every edge **Insphere** 5.774 mm across, touching every face **Surface area** 200.00 mm² **Volume** 192.45 mm³ **Sphere fill** 36.8% of its circumsphere **Isoperimetric quotient** 0.524 (a sphere is 1) **Weight at this size** 3.39 ct in diamond, 3.10 ct in moissanite **Orientation** Millimeters, Y up, one face resting on the ground plane, centered on the Y axis **Files** STEP, 3DM, STL, OBJ, FBX, GLB. 3D files only, no cutting files ## Cut Performance Index - Diamond not yet scored - Moissanite not yet scored - Cubic Zirconia not yet scored - Ruby not yet scored - Sapphire not yet scored - Emerald not yet scored - Amethyst not yet scored We have not set the census up for the Platonic solids. They are geometric models, not gem cuts, and we keep them out of the gem rankings. [See how every cut compares](https://digitalgemology.com/learn/cut-performance-index) ## Hexahedron: questions ### What files come with the Hexahedron 3D model? Six formats. STEP is the exact solid for CAD, and 3DM is for Rhino. STL and OBJ are meshes. FBX is for Blender, 3ds Max, Maya, Cinema 4D, Unity and Unreal. GLB is for the web and AR. All are in millimeters at real-world scale, with 6 flat faces. ### Is there a cutting file for the Hexahedron? No. We sell the Platonic solids as 3D models only, with no faceting design, tier table or diagram. ### How big is the Hexahedron model? Resting on a face, it measures 5.774 x 5.774 x 5.774 mm. Every vertex is on a sphere 10 mm across. All five Platonic solids share that sphere, so they nest and sit together at true relative size. You can scale it uniformly to any size: for a 10 mm edge, scale by 1.7321. ### How is the Hexahedron model oriented? Y up, with one face resting on the ground plane and the centroid on the Y axis. The midpoint of one edge of the resting face lies on the +X axis. This keeps the cube square to the axes. ### Can I 3D print or cast the Hexahedron model? Yes. The mesh is watertight and manifold, with outward normals and no duplicate vertices, so it prints and casts without repair. Use the STEP file when you need the exact solid in CAD. ## More Platonic solids - [Tetrahedron](https://digitalgemology.com/cuts/tetrahedron) - [Octahedron](https://digitalgemology.com/cuts/octahedron) - [Dodecahedron](https://digitalgemology.com/cuts/dodecahedron) - [Icosahedron](https://digitalgemology.com/cuts/icosahedron) ## Get the Hexahedron files *6 formats* *Millimeters* *Watertight* ### Hexahedron 3D files The hexahedron as exact geometry: 6 flat faces, real-world scale, ready for CAD, rendering, printing and casting. We sell the Platonic solids as 3D files only. - **STEP** Exact faceted solid for CAD - **3DM** Rhino, closed mesh on its own layer - **STL** Watertight mesh for printing and casting - **OBJ** Mesh for modeling and rendering - **FBX** Blender, 3ds Max, Maya, Cinema 4D, Unity, Unreal - **GLB** Web, AR and quick previews €3.99 · [Personal use](https://digitalgemology.com/licence) [Buy the 3D files](https://digitalgemology.lemonsqueezy.com/checkout/buy/55bffa20-ed7a-48b1-97a9-7cf09352071c) Save with a bundle: the hexahedron 3D files are also in [Platonic Solids Set](https://digitalgemology.com/cuts/#bundles), 5 solids for €7.49 until 1 December, then €9.99 (€19.95 as single files). [Buy the bundle](https://digitalgemology.lemonsqueezy.com/checkout/buy/a61992af-5c04-4d77-9edf-aff5a174e914?checkout%5Bdiscount_code%5D=BUNDLE25). These cube files are also free as a sample: [get them for your email address](https://digitalgemology.lemonsqueezy.com/checkout/buy/2d1ab55f-2bd6-4897-a4cd-f3320f54e99e), used only to send them ([privacy](https://digitalgemology.com/privacy#free-sample)). Questions before you buy? [Email us](mailto:support@digitalgemology.com).