# Isosceles triangle

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Isosceles triangle | |
---|---|

Rank | 2 |

Notation | |

Bowers style acronym | Isot |

Coxeter diagram | ox&#y |

Elements | |

Edges | 1+2 |

Vertices | 1+2 |

Vertex figure | Dyad |

Measures (edge lengths b [base], l [legs]) | |

Circumradius | |

Area | |

Angles | base–leg: |

leg–leg: | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Isot |

Regiment | Isot |

Dual | Isosceles triangle |

Conjugate | None |

Abstract & topological properties | |

Flag count | 6 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{1}×I, order 2 |

Convex | Yes |

Nature | Tame |

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, √ℓ
^{2}–*b*^{2}/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]}

Name | Picture | Edge lengths |
---|---|---|

Truncated tetrahedron | 1, √3, √3 | |

Truncated cube | 1, √2+√2, √2+√2 | |

Truncated octahedron | √2, √3, √3 | |

Quasitruncated hexahedron | 1, √2–√2, √2–√2 | |

Truncated dodecahedron | 1, √(5+√5)/2, √(5+√5)/2 | |

Truncated icosahedron | (√5+1)/2, √3, √3 | |

Truncated great dodecahedron | (√5–1)/2, √(5+√5)/2, √(5+√5)/2 | |

Truncated great icosahedron | (√5–1)/2, √3, √3 | |

Quasitruncated small stellated dodecahedron | (√5+1)/2, √(5–√5)/2, √(5–√5)/2 | |

Quasitruncated great stellated dodecahedron | 1, √(5–√5)/2, √(5–√5)/2 | |

Truncated square tiling | √2, √2+√2, √2+√2 | |

Truncated hexagonal tiling | 1, (√2+√6)/2, (√2+√6)/2 | |

Quasitruncated square tiling | √2, √2–√2, √2–√2 | |

Quasitruncated hexagonal tiling | 1, (√6–√2)/2, (√6–√2)/2 |

## References[edit | edit source]

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

## External links[edit | edit source]

- Wikipedia contributors. "Isosceles triangle".