Crossed isosceles trapezoid

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Crossed isosceles trapezoid
Rank2
Notation
Bowers style acronymCrotraz
Coxeter diagramx(–x)&#x
Elements
Edges1+1+2
Vertices2+2
Vertex figureDyad
Related polytopes
ArmyTraz
DualDart
ConjugateCrossed isosceles trapezoid
Abstract & topological properties
OrientableYes
Properties
SymmetryA1×I, order 2
ConvexNo
NatureTame

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:

Crossed trapezoids in vertex figures
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