Truncated triakis icosahedron explained

bgcolor=#e7dcc3 colspan=2	Truncated triakis icosahedron
align=center colspan=2
Conway notation	t10kI = dk10tD
Faces	12 decagons 60 pentagons
Edges	210
Vertices	140
Dual	Decakis truncated dodecahedron
Vertex configuration	12 (5.5.5) 60 (5.5.10)
Symmetry group	Ih
Properties	convex
Net

The truncated triakis icosahedron, or more precisely an order-10 truncated triakis icosahedron, is a convex polyhedron with 72 faces: 10 sets of 3 pentagons arranged in an icosahedral arrangement, with 12 decagons in the gaps.

Triakis icosahedron

It is constructed from a triakis icosahedron by truncating the order-10 vertices. This creates 12 regular decagon faces, and leaves 60 mirror-symmetric pentagons.

Decakis truncated dodecahedron

The dual of the truncated triakis icosahedron is called a decakis truncated dodecahedron. It can be seen as a truncated dodecahedron with decagonal pyramids augmented to the faces.

See also

• Truncated triakis tetrahedron
• Truncated triakis octahedron
• Truncated tetrakis cube

External links

• George Hart's Polyhedron generator - "t10kI" (Conway polyhedron notation)