--- title: "Icosahedron 3D Model: STEP, STL, OBJ, GLB" description: "The icosahedron as an exact 3D model in STEP, 3DM, STL, OBJ, FBX and GLB: 20 faces, 5.257 mm edges, 10 mm circumsphere." url: https://digitalgemology.com/cuts/icosahedron image: https://digitalgemology.com/img/cuts/icosahedron-og.jpg?v=e2c47a8a --- > Markdown copy of https://digitalgemology.com/cuts/icosahedron. 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) # Icosahedron **Buy (instant download, personal-use license):** [3D files · €3.99](https://digitalgemology.lemonsqueezy.com/checkout/buy/9843dc4f-c068-4b11-ace2-79e43a1e26f1) · [Icosahedron 3D files, €3.99 · Personal use](https://digitalgemology.lemonsqueezy.com/checkout/buy/9843dc4f-c068-4b11-ace2-79e43a1e26f1) · [Buy the bundle](https://digitalgemology.lemonsqueezy.com/checkout/buy/a61992af-5c04-4d77-9edf-aff5a174e914?checkout%5Bdiscount_code%5D=BUNDLE25) · [Get the cube free](https://digitalgemology.lemonsqueezy.com/checkout/buy/2d1ab55f-2bd6-4897-a4cd-f3320f54e99e) 3D model · 20 faces · 10 mm circumsphere Twenty equilateral triangles, meeting five at each of twelve vertices, dual to the dodecahedron. By isoperimetric quotient, it is the roundest of the five: it holds the most volume for its surface area. But the dodecahedron fills more of its own circumsphere. [3D files · €3.99](https://digitalgemology.lemonsqueezy.com/checkout/buy/9843dc4f-c068-4b11-ace2-79e43a1e26f1) Instant download · [Personal-use license](https://digitalgemology.com/licence) · [What is in the files](https://digitalgemology.com/cuts/icosahedron#buy) · [Open it in the Simulator](https://digitalgemology.com/tools/3d_gemstone_simulator?cut=icosahedron) ## About the icosahedron Twenty equilateral triangles, meeting five at each of twelve vertices, dual to the dodecahedron. By isoperimetric quotient, it is the roundest of the five: it holds the most volume for its surface area. But the dodecahedron fills more of its own circumsphere. Its fivefold symmetry rules it out as an ordinary crystal, as it does the dodecahedron. But icosahedral order does occur in quasicrystals, which are ordered but do not repeat. The first natural quasicrystal, now called icosahedrite, was reported in 2009. ## Icosahedron specifications Taken from the delivered model. We check it against its mesh every time we build this page. **Category** Platonic solids **Faces** 20 equilateral triangles, all congruent **Vertices** 12, 5 faces meeting at each **Edges** 30, each 5.257 mm **Schläfli symbol**{3,5} **Dual** The dodecahedron **Dihedral angle** 138.190°, the same on every edge **Size** 9.822 x 8.507 x 7.947 mm, resting on a face **Circumsphere** 10.000 mm across, through every vertex **Midsphere** 8.507 mm across, touching every edge **Insphere** 7.947 mm across, touching every face **Surface area** 239.36 mm² **Volume** 317.02 mm³ **Sphere fill** 60.5% of its circumsphere **Isoperimetric quotient** 0.829 (a sphere is 1) **Weight at this size** 5.58 ct in diamond, 5.10 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) ## Icosahedron: questions ### What files come with the Icosahedron 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 20 flat faces. ### Is there a cutting file for the Icosahedron? No. We sell the Platonic solids as 3D models only, with no faceting design, tier table or diagram. ### How big is the Icosahedron model? Resting on a face, it measures 9.822 x 8.507 x 7.947 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 1.9021. ### How is the Icosahedron 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 Icosahedron 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) - [Hexahedron](https://digitalgemology.com/cuts/hexahedron) - [Octahedron](https://digitalgemology.com/cuts/octahedron) - [Dodecahedron](https://digitalgemology.com/cuts/dodecahedron) ## Get the Icosahedron files *6 formats* *Millimeters* *Watertight* ### Icosahedron 3D files The icosahedron as exact geometry: 20 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/9843dc4f-c068-4b11-ace2-79e43a1e26f1) Save with a bundle: the icosahedron 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). Not sure the files open in your software? [Get the cube free](https://digitalgemology.lemonsqueezy.com/checkout/buy/2d1ab55f-2bd6-4897-a4cd-f3320f54e99e): the same six formats, for your email address, used only to send them ([privacy](https://digitalgemology.com/privacy#free-sample)). Questions before you buy? [Email us](mailto:support@digitalgemology.com).