| Hexagonal trapezohedron | |
|---|---|
 | |
| Type | trapezohedron |
| Faces | 12 kites |
| Edges | 24 |
| Vertices | 14 |
| Vertex configuration | V6.3.3.3 |
| Coxeter diagram |      |
| Symmetry group | D6d, [2+,12], (2*6), order 24 |
| Rotation group | D6, [2,6]+, (66), order 12 |
| Dual polyhedron | hexagonal antiprism |
| Properties | convex, face-transitive |
In geometry, a hexagonal trapezohedron or deltohedron is the fourth in an infinite series of trapezohedra which are dual polyhedra to the antiprisms. It has twelve faces which are congruent kites. It can be described by the Conway notation dA6.
It is an isohedral (face-transitive) figure, meaning that all its faces are the same. More specifically, all faces are not merely congruent but also transitive, i.e. lie within the same symmetry orbit. Convex isohedral polyhedra are the shapes that will make fair dice.[1]
- ^ McLean, K. Robin (1990), "Dungeons, dragons, and dice", The Mathematical Gazette, 74 (469): 243–256, doi:10.2307/3619822, JSTOR 3619822.