Archimedean Solids · 3D
Truncated Cube
3.8.8 · t{4,3}
Slice the eight corners off a cube until every square becomes a regular octagon. Eight small triangles appear where the corners were.
- Vertices
- 24
- Edges
- 36
- Triangles
- 8
- Octagons
- 6
Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane.
Facts
- For regular octagons the cut runs 1 − 1/√2 ≈ 0.293 of the way along each edge.
- Across its octagons it measures 1 + √2 edges: the silver ratio, which the octagon holds as the pentagon holds φ.
- Every corner joins one triangle and two octagons (3.8.8).
- Its dual, the triakis octahedron, is an octahedron with a low pyramid raised on every face.
History and meaning
Renaissance artists drew the cut solids as exercises in perspective. Wenzel Jamnitzer’s Perspectiva Corporum Regularium (1568) is a whole book of them, turned, hollowed and stellated.
Across the dimensions
- Its slice The Sacred CutThe octagon of the sacred cut is a face of the truncated cube: lay the cut on every face of a cube and slice away its corners.
- Dual The triakis octahedron, which the app draws inside it.
