Great triambic icosahedron: Difference between revisions
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== Medial triambic icosahedron == |
== Medial triambic icosahedron == |
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The '''medial triambic icosahedron''' is the dual of the [[ditrigonal dodecadodecahedron]], U41. It has 20 faces, each being concave [[Isogonal figure|isogonal]] [[hexagon]]s. It has 24 vertices: 12 exterior points, and 12 hidden inside. It has 60 edges. |
The '''medial triambic icosahedron''' is the dual of the [[ditrigonal dodecadodecahedron]], U41. It has 20 faces, each being simple concave [[Isogonal figure|isogonal]] [[hexagon]]s. It has 24 vertices: 12 exterior points, and 12 hidden inside. It has 60 edges. |
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== As a stellation == |
== As a stellation == |
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Revision as of 17:16, 25 May 2011
| Great triambic icosahedron and Medial triambic icosahedron | ||
| ||
| Types | Dual uniform polyhedra | |
| Symmetry group | Ih | |
| Name | Great triambic icosahedron | Medial triambic icosahedron |
| Index references | DU47 | DU41 |
| Elements | F = 20, E = 60 V = 32 (χ = -8) |
F = 20, E = 60 V = 24 (χ = -16) |
| Isohedral faces |  |
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| Duals |  Great ditrigonal icosidodecahedron |
 Ditrigonal dodecadodecahedron |
| Stellation | ||
| Icosahedron: W34 | ||
 Stellation diagram | ||
In geometry, the great triambic icosahedron and medial triambic icosahedron are a visually identical dual uniform polyhedra. The exterior surface also represents a stellation of the icosahedron.
The 12 vertices of the convex hull matches the vertex arrangement of an icosahedron.
Great triambic icosahedron
The great triambic icosahedron is the dual of the great ditrigonal icosidodecahedron, U47. It has 20 inverted-hexagonal faces, shaped like a three-bladed propeller. It has 32 vertices: 12 exterior points, and 20 hidden inside. It has 60 edges.
Medial triambic icosahedron
The medial triambic icosahedron is the dual of the ditrigonal dodecadodecahedron, U41. It has 20 faces, each being simple concave isogonal hexagons. It has 24 vertices: 12 exterior points, and 12 hidden inside. It has 60 edges.
As a stellation
It is Wenninger's 34th model in his 9th stellation of the icosahedron
See also
References
- Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9.
- Wenninger, Magnus (1983). Dual Models. Cambridge University Press. ISBN 978-0-521-54325-5. MR730208.
External links
- Weisstein, Eric W. "Great triambic icosahedron". MathWorld.
- Weisstein, Eric W. "Medial triambic icosahedron". MathWorld.
- gratrix.net Uniform polyhedra and duals
- bulatov.org Medial triambic icosahedron Great triambic icosahedron
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