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Regular icosahedron
(Click here for rotatin model)
Type Platonic solid
Elements F = 20, E = 30
V = 12 (χ = 2)
Faces by sides 20{3}
Conway notation {{{I-conway}}}
Schläfli seembols {3,5}
s{3,4}, sr{3,3}
Face confeeguration {{{I-ffig}}}
Wythoff seembol 5 | 2 3
Coxeter diagram CDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node 1.png
Symmetry Ih, H3, [5,3], (*532)
Rotation group I, [5,3]+, (532)
References U22, C25, W4
Properties regular, convexdeltahedron
Dihedral angle 138.189685° = arccos(-√5/3)
Icosahedron vertfig.svg
(Vertex feegur)
(dual polyhedron)
Icosahedron flat.svg

In geometry, an icosahedron (/ˌksəˈhdrən/ or /ˌkɒsəˈhdrən/) 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 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" (-/drə/).