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|bgcolor=#e7dcc3|Vertices||28
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|bgcolor=#e7dcc3|Dual|[[Hexakis truncated tetrahedron]]
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|bgcolor=#e7dcc3|[[Vertex configuration]]||4 (5.5.5)<BR>24 (5.5.6)
|bgcolor=#e7dcc3|[[Vertex configuration]]||4 (5.5.5)<BR>24 (5.5.6)
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A topologically similar [[equilateral]] polyhedron can be constructed by using 12 [[Regular polygon|regular]] pentagons with 4 [[equilateral]] but nonplanar hexagons, each vertex with [[internal angle]]s alternating between 108 and 132 degrees.
A topologically similar [[equilateral]] polyhedron can be constructed by using 12 [[Regular polygon|regular]] pentagons with 4 [[equilateral]] but nonplanar hexagons, each vertex with [[internal angle]]s alternating between 108 and 132 degrees.


==Full Truncation==
A Triakis Tetrahedron can be fully truncated, not giving out this. The Full truncation is a special type of icosahedron, rather than a hexadecahedron. Another alternate truncation, or the "Low order truncation", will give out what looks like a [[Tetrahedron]] with each face raised by a low [[Pyramidal frustum|Triangular frustum]]. The dual to that truncation will be the "Triakis Truncated Tetrahedron". However, the full truncation is dual to a ''Trihexakis truncated tetrahedron''.
[[Image:Truncated triakis tetrahedron.png|240px|The common truncation]] [[File:StellaTruncTriakisTetra.png|120px|The Full Truncation]]
== See also ==
== See also ==
* [[Near-miss Johnson solid]]
* [[Near-miss Johnson solid]]

Revision as of 19:05, 25 May 2011

Truncated triakis tetrahedron
Truncated triakis tetrahedron
Type Conway polyhedron
Faces 4 hexagons
12 pentagons
Edges 42
Vertices 28
Dual|Hexakis truncated tetrahedron
Vertex configuration 4 (5.5.5)
24 (5.5.6)
Symmetry group Td
Properties convex

The 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. It is constructed from taking a triakis tetrahedron by truncating the order-6 vertices. This creates 4 regular hexagon faces, and leaves 12 irregular pentagons.

A topologically similar equilateral polyhedron can be constructed by using 12 regular pentagons with 4 equilateral but nonplanar hexagons, each vertex with internal angles alternating between 108 and 132 degrees.

Full Truncation

A Triakis Tetrahedron can be fully truncated, not giving out this. The Full truncation is a special type of icosahedron, rather than a hexadecahedron. Another alternate truncation, or the "Low order truncation", will give out what looks like a Tetrahedron with each face raised by a low Triangular frustum. The dual to that truncation will be the "Triakis Truncated Tetrahedron". However, the full truncation is dual to a Trihexakis truncated tetrahedron. The common truncation The Full Truncation

See also