# Isosceles trapezoid

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.

Isosceles trapezoid
Rank2
SpaceSpherical
Notation
Bowers style acronymTraz
Coxeter diagramxy&#z
Elements
Edges1+1+2
Vertices2+2
Measures (edge lengths ${\displaystyle b_1}$ (small base), ${\displaystyle b_2}$ (large base), ℓ (lacing))
Area${\displaystyle \frac{b_1+b_2}{2}\sqrt{l^2-\frac{b_2-b_1}{2}^2}}$
Height${\displaystyle \sqrt{l^2-\frac{b_2-b_1}{2}^2}}$
Central density1
Related polytopes
ArmyTraz
DualKite
ConjugateIsosceles trapezoid
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryA1×I, order 2
ConvexYes
NatureTame

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

## In vertex figures

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