Archimedean Solids · 3D
Truncated Dodecahedron
3.10.10 · t{5,3}
Slice the twenty corners off a dodecahedron until each pentagon becomes a regular decagon. Twenty small triangles sit where the corners were.
- Vertices
- 60
- Edges
- 90
- Triangles
- 20
- Decagons
- 12
Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane.
Facts
- For regular decagons the cut runs 1/(φ√5) ≈ 0.276 of the way along each edge.
- Every corner joins one triangle and two decagons (3.10.10).
- Cut deeper and the decagons shrink to pentagons again: the icosidodecahedron.
- Its dual, the triakis icosahedron, is an icosahedron with a low pyramid on every face.
History and meaning
Kepler drew it in Harmonices Mundi (1619), where he proved that apart from the endless prisms and antiprisms there are exactly thirteen such solids.
Across the dimensions
- Dual The triakis icosahedron, which the app draws inside it.
