Hexagonal bipyramid
Hexagonal bipyramid | |
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face-transitive |
A hexagonal bipyramid is a polyhedron formed from two hexagonal pyramids joined at their bases. The resulting solid has 12 triangular faces, 8 vertices and 18 edges. The 12 faces are identical isosceles triangles.
Although it is
It is one of an infinite set of bipyramids. Having twelve faces, it is a type of dodecahedron, although that name is usually associated with the regular polyhedral form with pentagonal faces.
The hexagonal bipyramid has a
Images
It can be drawn as a tiling on a sphere which also represents the fundamental domains of [3,2], *322
Related polyhedra
The hexagonal bipyramid, dt{2,6}, can be in sequence truncated, tdt{2,6} and alternated (snubbed), sdt{2,6}:
The hexagonal bipyramid, dt{2,6}, can be in sequence rectified, rdt{2,6}, truncated, trdt{2,6} and alternated (snubbed), srdt{2,6}:
Uniform hexagonal dihedral spherical polyhedra | ||||||||||||||
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[6,2] , (*622)
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[6,2]+, (622) | [6,2+], (2*3) | ||||||||||||
{6,2} | t{6,2} | r{6,2} | t{2,6} | {2,6} | rr{6,2} | tr{6,2} | sr{6,2} | s{2,6} | ||||||
Duals to uniforms | ||||||||||||||
V62 | V122 | V62 | V4.4.6 | V26 | V4.4.6 | V4.4.12 | V3.3.3.6 | V3.3.3.3 |
It is the first polyhedra in a sequence defined by the
With an even number of faces at every vertex, these polyhedra and tilings can be shown by alternating two colors so all adjacent faces have different colors.
Each face on these domains also corresponds to the fundamental domain of a symmetry group with order 2,3,n mirrors at each triangle face vertex.
*n32 symmetry mutation of omnitruncated tilings: 4.6.2n | ||||||||||||
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Sym. *n32 [n,3] |
Spherical | Euclid. | Compact hyperb. | Paraco. | Noncompact hyperbolic | |||||||
*232 [2,3] |
*332 [3,3] |
*432 [4,3] |
*532 [5,3] |
*632 [6,3] |
*732 [7,3] |
*832 [8,3] |
*∞32 [∞,3] |
[12i,3] |
[9i,3] |
[6i,3] |
[3i,3] | |
Figures | ||||||||||||
Config. | 4.6.4 | 4.6.6 | 4.6.8 | 4.6.10 | 4.6.12 | 4.6.14 | 4.6.16 | 4.6.∞ | 4.6.24i | 4.6.18i | 4.6.12i | 4.6.6i |
Duals | ||||||||||||
Config.
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V4.6.4 | V4.6.6 | V4.6.8 | V4.6.10 | V4.6.12
|
V4.6.14
|
V4.6.16
|
V4.6.∞ | V4.6.24i | V4.6.18i | V4.6.12i | V4.6.6i |
Bipyramid name |
Digonal bipyramid |
Triangular bipyramid |
Square
bipyramid |
Pentagonal bipyramid |
Hexagonal bipyramid |
... | Apeirogonal
bipyramid |
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Polyhedron image |
... | ||||||
Spherical tiling image |
Plane tiling image |
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Face config.
|
V2.4.4 | V3.4.4 | V4.4.4 | V5.4.4 | V6.4.4 | ... | V∞.4.4 |
Coxeter
diagram |
... |
See also
- hexagonal trapezohedron A similar 12-sided polyhedron with a twist and kite faces.
- Snub disphenoid Another 12-sided polyhedron with 2-fold symmetry and only triangular faces.
External links
- Weisstein, Eric W. "Dipyramid". MathWorld.
- Virtual Reality Polyhedra The Encyclopedia of Polyhedra
- VRML model hexagonal dipyramid
- Conway Notation for Polyhedra Try: dP6