Truncated icosahedron

Truncated icosahedron
Dimensionality	3
Schläfli Symbol	'"`UNIQ--postMath-00000001-QINU`"'
Coxeter–Dynkin diagram
Bowers acronym	ti
Subfacets
Vertices	60 points
Edges	90 line segments
Faces	12 pentagons 20 hexagons
Cells	1 truncated icosahedron
Hypervolumes
Vertex Count	'"`UNIQ--postMath-00000002-QINU`"'
Edge Length	'"`UNIQ--postMath-00000003-QINU`"'
Surface Area	'"`UNIQ--postMath-00000004-QINU`"'
Surcell Volume	'"`UNIQ--postMath-00000005-QINU`"'

The truncated icosahedron is the three-dimensional uniform polyhedron produced by truncating an icosahedron. Each vertex of the icosahedron becomes a pentagonal face in the truncated icosahedron and each triangular face becomes a hexagonal face. Its Bowers' acronym is ti.

It can also be constructed through bitruncating a dodecahedron.

Its dual is the triakis icosahedron.

It is well-known as the shape of an association football or soccer ball.

Structure and Sections

Subfacets

• 60 points (0D)
• 90 line segments (1D)
• 12 pentagons (2D)
• 20 hexagons (2D)
• 1 truncated icosahedron (3D)

Hypervolumes

• vertex count = $60$
• edge length = $90l$
• surface area = $\left(30{\sqrt {3}}+15{\sqrt {1+{\frac {2}{\sqrt {5}}}}}\right)l^{2}$
• surcell volume = ${\frac {125+43{\sqrt {5}}}{4}}l^{3}$

See Also

Regular $t_0 \{5,3\}$	Rectified $t_1 \{5,3\}$	Birectified $t_2 \{5,3\}$	Truncated $t_{0,1} \{5,3\}$	Bitruncated $t_{1,2} \{5,3\}$	Cantellated $t_{0,2} \{5,3\}$	Cantitruncated $t_{0,1,2} \{5,3\}$
Dodecahedron	Icosidodecahedron	Icosahedron	Truncated dodecahedron	Truncated icosahedron	Rhombicosidodecahedron	Great rhombicosidodecahedron