Kepler–Poinsot Solids · 3D
Great Icosahedron
{3, 5/2}
Twenty great triangles through the icosahedron’s corners, each spanning two of its edges, crossing into a dense crystal. Five meet at every point.
- Vertices
- 12
- Edges
- 30
- Faces
- 20 ▲
- Density
- 7
Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane.
Facts
- It has exactly the frame of the small stellated dodecahedron, the same 12 corners and 30 edges, closed with triangles instead of pentagrams.
- Its faces lie in the planes of the icosahedron’s faces: it is one of the icosahedron’s 59 stellations.
- Its faces wrap its centre seven times: its density is 7.
- Its dual is the great stellated dodecahedron.
History and meaning
Poinsot described it in 1809. It is the only one of the four with triangular faces, and the hardest to see: nearly all of each triangle is hidden inside the others.
Across the dimensions
Learn it step by step
- Journey Kepler’s StarsStep 6: Stars of triangles
