Triangular orthobicupola
Triangular orthobicupola | |
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squares | |
Edges | 24 |
Vertices | 12 |
Vertex configuration | 6(32.42) 6(3.4.3.4) |
Symmetry group | D3h |
Dual polyhedron | Trapezo-rhombic dodecahedron |
Properties | convex |
Net | |
In
A
The triangular orthobicupola is the first in an infinite set of orthobicupolae.
Relation to cuboctahedra
Triangular orthobicupola | Triangular gyrobicupola |
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Both the triangular orthobicupola and the cuboctahedron (triangular gyrobicupola) contain a central regular hexagon. They can be dissected on this hexagon into pairs of triangular cupolae. |
The triangular orthobicupola has a superficial resemblance to the cuboctahedron, which would be known as the triangular gyrobicupola in the nomenclature of Johnson solids — the difference is that the two triangular cupolas which make up the triangular orthobicupola are joined so that pairs of matching sides abut (hence, "ortho"); the cuboctahedron is joined so that triangles abut squares and vice versa. Given a triangular orthobicupola, a 60-degree rotation of one cupola before the joining yields a cuboctahedron. Hence, another name for the triangular orthobicupola is the anticuboctahedron.
The elongated triangular orthobicupola (J35), which is constructed by elongating this solid, has a (different) special relationship with the rhombicuboctahedron.
The dual of the triangular orthobicupola is the trapezo-rhombic dodecahedron. It has 6 rhombic and 6 trapezoidal faces, and is similar to the rhombic dodecahedron.
Formulae
The following formulae for volume, surface area, and circumradius can be used if all faces are regular, with edge length a:[2]
The circumradius of a triangular orthobicupola is the same as the edge length (C = a).
Related polyhedra and honeycombs
The
References
- Zbl 0132.14603.
- Wolfram Alpha. Retrieved July 23, 2010.
- ^ "J27 honeycomb".