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.
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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.
Taken from the delivered model. We check it against its mesh every time we build this page.
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.
No. We sell the Platonic solids as 3D models only, with no faceting design, tier table or diagram.
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.
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.
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.
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.
Save with a bundle: the icosahedron 3D files are also in Platonic Solids Set, 5 solids for €7.49 until 1 December, then €9.99 (€19.95 as single files). Buy the bundle.
Not sure the files open in your software? Get the cube free: the same six formats, for your email address, used only to send them (privacy).
Questions before you buy? Email us.