3D model · 20 faces · 10 mm circumsphere
Twenty equilateral triangles, meeting five at each of twelve vertices, dual to the dodecahedron. It is the roundest of the five by isoperimetric quotient, holding the most volume for its surface area, although 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. It is the roundest of the five by isoperimetric quotient, holding the most volume for its surface area, although the dodecahedron fills more of its own circumsphere.
Its fivefold symmetry rules it out as an ordinary crystal, as it does the dodecahedron. Icosahedral order does occur in quasicrystals, which are ordered without repeating; the first natural one, now called icosahedrite, was reported in 2009.
Taken from the delivered model and checked against its mesh every time this page is built.
Six formats: STEP (the exact solid for CAD), 3DM for Rhino, STL and OBJ meshes, FBX for Blender, 3ds Max, Maya, Cinema 4D, Unity and Unreal, and GLB for the web and AR. All are in millimetres at real-world scale, with 20 flat faces.
No. The Platonic solids are sold as 3D models only, with no faceting design, tier table or diagram.
It measures 9.822 x 8.507 x 7.947 mm resting on a face, with every vertex on a sphere 10 mm across. All five Platonic solids share that sphere, so they nest and sit together at true relative size. 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, which 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. The Platonic solids are sold as 3D files only.
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