Truncated triakis tetrahedron: Difference between revisions
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|bgcolor=#e7dcc3|Vertices||28 |
|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. |
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==Full Truncation== |
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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''. |
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[[Image:Truncated triakis tetrahedron.png|240px|The common truncation]] [[File:StellaTruncTriakisTetra.png|120px|The Full Truncation]] |
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== See also == |
== See also == |
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* [[Near-miss Johnson solid]] |
* [[Near-miss Johnson solid]] |
Revision as of 19:05, 25 May 2011
Truncated triakis tetrahedron | |
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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.