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An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties.
The relations can be made apparent by examining the vertex figures obtained by listing the faces adjacent to each vertex (remember that for uniform polyhedra all vertices are the same, that is vertex-transitive). For example, the cube has vertex figure 4.4.4, which is to say, three adjacent square faces. The possible faces are 3 - equilateral ...
The truncated tetrahedron can be constructed from a regular tetrahedron by cutting all of its vertices off, a process known as truncation. [1] The resulting polyhedron has 4 equilateral triangles and 4 regular hexagons, 18 edges, and 12 vertices. [2] With edge length 1, the Cartesian coordinates of the 12 vertices are points
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
A deltahedron is a polyhedron whose faces are all equilateral triangles. The deltahedron is named by Martyn Cundy, after the Greek capital letter delta resembling a triangular shape Δ. [1] The deltahedron can be categorized by the property of convexity. The simplest convex deltahedron is the regular tetrahedron, a pyramid with four equilateral ...
Broken down, 3 6; 3 6 (both of different transitivity class), or (3 6) 2, tells us that there are 2 vertices (denoted by the superscript 2), each with 6 equilateral 3-sided polygons (triangles). With a final vertex 3 4.6, 4 more contiguous equilateral triangles and a single regular hexagon.
Regular complex apeirogons have vertices and edges, where edges can contain 2 or more vertices. Regular apeirogons p{q}r are constrained by: 1/p + 2/q + 1/r = 1. Edges have p vertices, and vertex figures are r-gonal. [5] The first is made of 2-edges, and next two are triangular edges, and the last has overlapping hexagonal edges.
The Archimedean solids have a single vertex configuration and highly symmetric properties. A vertex configuration indicates which regular polygons meet at each vertex. For instance, the configuration indicates a polyhedron in which each vertex is met by alternating two triangles and two pentagons.
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