Diminished trapezohedron
In geometry, a diminished trapezohedron is a polyhedron in an infinite set of polyhedra, constructed by removing one of the polar vertices of a trapezohedron and replacing it by a new face (diminishment). It has one regular n-gonal base face, n triangle faces around the base, and n kites meeting on top. The kites can also be replaced by rhombi with specific proportions.
| Diminished trapezohedron | |
|---|---|
Example square form | |
| Faces | n kites n triangles 1 n-gon |
| Edges | 4n |
| Vertices | 2n + 1 |
| Symmetry group | Cnv, [n], (*nn) |
| Rotation group | Cn, [n]+, (nn) |
| Dual polyhedron | self-dual |
| Properties | convex |
Along with the set of pyramids and elongated pyramids, these figures are topologically self-dual.
It can also be seen as an augmented n-gonal antiprism, with a n-gonal pyramid augmented onto one of the n-gonal faces, and whose height is adjusted so the upper antiprism triangle faces can be made coparallel to the pyramid faces and merged into kite-shaped faces.
They're also related to the gyroelongated pyramids, as augmented antiprisms and which are Johnson solids for n = 4, 5. This sequence has sets of two triangles instead of kite faces.