# Icosahedron

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Regular Icosahedron

Type Platonic solid
Elements F = 20, E = 30
V = 12 (χ = 2)
Faces bi sides 20{3}
Schläfli seembols {3,5}
s{3,4}, sr{3,3}
Wythoff seembol 5 | 2 3
Coxeter diagram
Symmetry Ih, H3, [5,3], (*532)
Rotation group I, [5,3]+, (532)
References U22, C25, W4
Properties Regular convex deltahedron
Dihedral angle 138.189685° = arccos(-√5/3)

3.3.3.3.3
(Vertex figure)

Dodecahedron
(dual polyhedron)

Net

In geometry, an icosahedron ( or ) is a polyhedron wi 20 triangular faces, 30 edges an 12 vertices. A regular icosahedron wi identical equilateral faces is eften meant acause o its geometrical signeeficance as ane o the five Platonic solids.

It haes five triangular faces meetin at each vertex. It can be representit bi its vertex figure as 3.3.3.3.3 or 35, an an aa bi Schläfli seembol {3,5}. It is the dual o the dodecahedron, which is representit bi {5,3}, havin three pentagonal faces aroond each vertex.

A regular icosahedron is a gyroelongated pentagonal bipyramid an a biaugmented pentagonal antiprism in ony o sax orientations.

The name comes frae the Greek: εικοσάεδρον, frae είκοσι (eíkosi) "twenty" an ἕδρα (hédra) "seat". The plural can be either "icosahedrons" or "icosahedra" (-).