Anonymous ID: 1e1e0e Dec. 3, 2018, 12:22 a.m. No.4126365   🗄️.is đź”—kun   >>6426

>>4126352

Truncated icosahedron

Truncatedicosahedron.jpg

(Click here for rotating model)

Type Archimedean solid

Uniform polyhedron

Elements F = 32, E = 90, V = 60 (χ = 2)

Faces by sides 12{5}+20{6}

Conway notation tI

Schläfli symbols t{3,5}

t0,1{3,5}

Wythoff symbol 2 5 | 3

Coxeter diagram CDel node.pngCDel 5.pngCDel node 1.pngCDel 3.pngCDel node 1.png

Symmetry group Ih, H3, [5,3], (*532), order 120

Rotation group I, [5,3]+, (532), order 60

Dihedral angle 6-6: 138.189685°

6-5: 142.62°

References U25, C27, W9

Properties Semiregular convex

Polyhedron truncated 20 max.png

Colored faces Truncated icosahedron vertfig.png

5.6.6

(Vertex figure)

Polyhedron truncated 20 dual max.png

Pentakis dodecahedron

(dual polyhedron) Polyhedron truncated 20 net.svg

Net

In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose faces are two or more types of regular polygons.

 

It has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges.

 

It is the Goldberg polyhedron GPV(1,1) or {5+,3}1,1, containing pentagonal and hexagonal faces.

 

This geometry is associated with footballs typically patterned with white hexagons and black pentagons