Isosceles trapezoid

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Isosceles trapezoid
Rank2
Notation
Bowers style acronymTraz
Coxeter diagramxy&#z
Elements
Edges1+1+2
Vertices2+2
Vertex figureDyad
Measures (edge lengths  (small base), (large base), ℓ (lacing))
Area
Height
Central density1
Related polytopes
ArmyTraz
DualKite
ConjugateIsosceles trapezoid
Abstract & topological properties
Flag count8
Euler characteristic0
OrientableYes
Properties
SymmetryA1×I, order 2
ConvexYes
NatureTame

The isosceles trapezoid is a trapezoid with a single symmetry axis. Equivalently, it is a trapezoid with the same leg lengths and base angles. It has 1 top edge, 2 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.

If the legs intersect, the figure may more precisely be called a crossed isosceles trapezoid.

In vertex figures[edit | edit source]

Every polygonal antiprism has an isosceles trapezoid as its vertex figure. The vertex figures for the crossed antiprisms are themselves crossed, and thus crossed isosceles trapezoids. Seven other uniform polyhedra have trapezoidal vertex figures.

Isosceles trapezoids in vertex figures
Name Picture Edge lengths
Triangular antiprism
1, 1, 1, 1
Square antiprism
1, 1, 1, 2
Pentagonal antiprism
1, 1, 1, (5+1)/2
Pentagrammic antiprism
1, 1, 1, (5–1)/2
Hexagonal antiprism
1, 1, 1, 3
...
Small rhombicuboctahedron
1, 2, 2, 2
Great cubicuboctahedron
1, 2-2, 2, 2-2
Small rhombicosidodecahedron
1, 2, (1+5)/2, 2
Great dodecicosidodecahedron
1, (5-5)/2, (5-1)/2, (5-5)/2
Rhombidodecadodecahedron
(5-1)/2, 2, (1+5)/2, 2
Small icosicosidodecahedron
1, 3, (5-1)/2, 3
Great ditrigonal dodecicosidodecahedron
1, (5–5)/2, (1+5)/2, (5–5)/2