Isosceles triangle

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Isosceles triangle
Isosceles triangle.svg
Rank2
SpaceSpherical
Bowers style acronymIsot
Coxeter diagramox&#y
Elements
Vertex figureDyad
Edges1+2
Vertices1+2
Measures (edge lengths b [base], ℓ [legs])
Circumradius
Area
Anglesbase–leg:
 leg–leg:
Height
Central density1
Euler characteristic0
Related polytopes
ArmyIsot
RegimentIsot
DualIsosceles triangle
ConjugateIsosceles triangle
Topological properties
OrientableYes
Properties
SymmetryA1×I, order 2
ConvexYes
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[edit | edit source]

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[edit | edit source]

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.[1]

Isosceles triangles in vertex figures
Name Picture Edge lengths
Truncated tetrahedron
Truncated tetrahedron.png
1, 3, 3
Truncated cube
Truncated hexahedron.png
1, 2+2, 2+2
Truncated octahedron
Truncated octahedron.png
2, 3, 3
Quasitruncated hexahedron
Stellated truncated hexahedron.png
1, 2–2, 2–2
Truncated dodecahedron
Truncated dodecahedron.png
1, (5+5)/2, (5+5)/2
Truncated icosahedron
Truncated icosahedron.png
(5+1)/2, 3, 3
Truncated great dodecahedron
Great truncated dodecahedron.png
(5–1)/2, (5+5)/2, (5+5)/2
Truncated great icosahedron
Great truncated icosahedron.png
(5–1)/2, 3, 3
Quasitruncated small stellated dodecahedron
Small stellated truncated dodecahedron.png
(5+1)/2, (5–5)/2, (5–5)/2
Quasitruncated great stellated dodecahedron
Great stellated truncated dodecahedron.png
1, (5–5)/2, (5–5)/2

References[edit | edit source]

  1. McCooey, David I. "Self-Intersecting Truncated Regular Polyhedra".

External links[edit | edit source]