Crossed isosceles trapezoid
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| Crossed isosceles trapezoid | |
|---|---|
 | |
| Rank | 2 |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Crotraz |
| Coxeter diagram | x(–x)&#x |
| Elements | |
| Edges | 1+1+2 |
| Vertices | 2+2 |
| Vertex figure | Dyad |
| Related polytopes | |
| Army | Traz |
| Dual | Dart |
| Conjugate | Crossed isosceles trapezoid |
| Topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | A1×I, order 2 |
| Convex | No |
| Nature | Tame |
The crossed isosceles trapezoid is a crossed trapezoid with a single symmetry axis. Equivalently, it is a crossed trapezoid with the same leg lengths and base angles. It has 1 top edge, 2 intersecting side edges of the same length, and 1 base edge. It has 2 pairs of identical vertices, as the angles at either end of the bases are the same.
In vertex figures[edit | edit source]
The crossed antiprisms have crossed isosceles trapezoids for vertex figures, along with 7 other uniform polyhedra:
| Name | Picture | Edge lengths |
|---|---|---|
| Quasirhombicuboctahedron |  |
1, √2, √2, √2 |
| Small cubicuboctahedron |  |
1, √2+√2, √2, √2+√2 |
| Quasirhombicosidodecahedron |  |
1, √2, (√5–1)/2, √2 |
| Icosidodecadodecahedron |  |
(√5–1)/2, √3, (1+√5)/2, √3 |
| Small dodecicosidodecahedron |  |
1, √(5+√5)/2, (1+√5)/2, √(5+√5)/2 |
| Great icosicosidodecahedron |  |
1, √3, (1+√5)/2, √3 |
| Small ditrigonal dodecicosidodecahedron |  |
1, √(5+√5)/2, (√5–1)/2, √(5+√5)/2 |