# Isosceles triangle

Isosceles triangle Rank2
SpaceSpherical
Bowers style acronymIsot
Info
Coxeter diagramox&#y
SymmetryA1×I, order 2
ArmyIsot
RegimentIsot
Elements
Edges1+2
Vertices1+2
Measures (edge lengths b [base], ℓ [legs])
Circumradius$\frac{l^2}{2\sqrt{l^2-\frac{b^2}{4}}}$ Area$\frac{b}{2}\sqrt{l^2-\frac{b^2}{4}}$ Anglesbase–leg: $\arccos\left(\frac{b}{2l}\right)$ leg–leg: $2\arcsin\left(\frac{b}{2l}\right)$ Height$\sqrt{l^2-\frac{b^2}{4}}$ Central density1
Euler characteristic0
Related polytopes
DualIsosceles triangle
ConjugateIsosceles triangle
Properties
ConvexYes
OrientableYes
NatureTame

The isosceles triangle, or isot, is a type of triangle with two of the three side lengths equal, as are two of the three angles. It can be considered as a pyramid where the base is a dyad.

Its unequal side is often called its base, in analogy to the pyramid construction. Its equal sides are called its legs.

## Vertex coordinates

Coordinates for an isosceles triangle with base length b and leg length ℓ are given by:

• b/2, 0),
• (0, 2b2/4).

## In vertex figures

All regular polygonal prisms have an isosceles triangle for a vertex figure. Polyhedra with isosceles vertex figures are sometimes known as truncated regular polyhedra, as they all derive from truncations of other polyhedra.