Trapezohedron
In geometry, an n-gonal trapezohedron, n-trapezohedron, n-antidipyramid, n-antibipyramid, or n-deltohedron is the dual polyhedron of an n-gonal antiprism. The 2n faces of an n-trapezohedron are congruent and symmetrically staggered; they are called twisted kites. With a higher symmetry, its 2n faces are kites (also called deltoids).
| Set of dual-uniform n-gonal trapezohedra | |
|---|---|
Example: dual-uniform pentagonal trapezohedron (n = 5) | |
| Type | dual-uniform in the sense of dual-semiregular polyhedron |
| Faces | 2n congruent kites |
| Edges | 4n |
| Vertices | 2n + 2 |
| Vertex configuration | V3.3.3.n |
| Schläfli symbol | { } ⨁ {n} |
| Conway notation | dAn |
| Coxeter diagram | |
| Symmetry group | Dnd, [2+,2n], (2*n), order 4n |
| Rotation group | Dn, [2,n]+, (22n), order 2n |
| Dual polyhedron | (convex) uniform n-gonal antiprism |
| Properties | convex, face-transitive, regular vertices |
The "n-gonal" part of the name does not refer to faces here, but to two arrangements of each n vertices around an axis of n-fold symmetry. The dual n-gonal antiprism has two actual n-gon faces.
An n-gonal trapezohedron can be dissected into two equal n-gonal pyramids and an n-gonal antiprism.
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