The truncated triakis icosahedron, or more precisely an order-10 truncated
triakis icosahedron
In geometry, the triakis icosahedron (or kisicosahedronConway, Symmetries of things, p.284) is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated dodecahedron.
Cartesian coordinates
Let \phi be the golden ratio. The 12 po ...
, is a convex polyhedron with 72 faces: 10 sets of 3
pentagon
In geometry, a pentagon (from the Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°.
A pentagon may be simpl ...
s arranged in an
icosahedral
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
arrangement, with 12
decagons in the gaps.
Triakis icosahedron
It is constructed from taking a
triakis icosahedron
In geometry, the triakis icosahedron (or kisicosahedronConway, Symmetries of things, p.284) is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated dodecahedron.
Cartesian coordinates
Let \phi be the golden ratio. The 12 po ...
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
In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges.
Geometric relations
This polyhedron can be formed from a regular dodecahedron by truncat ...
with
decagonal pyramid
In geometry, a pyramid () is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a ''lateral face''. It is a conic solid with polygonal base. A pyramid with an base ...
s augmented to the faces.
See also
*
Truncated triakis tetrahedron
In geometry, the truncated triakis tetrahedron, or more precisely an order-6 truncated triakis tetrahedron, is a convex polyhedron with 16 faces: 4 sets of 3 pentagons arranged in a tetrahedral arrangement, with 4 hexagons in the gaps.
Cons ...
*
Truncated triakis octahedron
The truncated triakis octahedron, or more precisely an order-8 truncated triakis octahedron, is a convex polyhedron with 30 faces: 8 sets of 3 pentagons arranged in an octahedral symmetry, octahedral arrangement, with 6 octagons in the gaps.
Tria ...
*
Truncated tetrakis cube
The truncated tetrakis cube, or more precisely an order-6 truncated tetrakis cube or hexatruncated tetrakis cube, is a convex polyhedron with 32 faces: 24 sets of 3 bilateral symmetry pentagons arranged in an octahedral arrangement, with 8 regular ...
External links
George Hart's Polyhedron generator- "t10kI" (
Conway polyhedron notation)
Polyhedra
Truncated tilings
{{Polyhedron-stub