Set of cupolae | |
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Example: pentagonal orthobirotunda
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Faces | 2n-gons 2n pentagons 4n triangles |
Edges | 12n |
Vertices | 6n |
Symmetry group | Ortho: Dnh, [n,2], (*n22), order 4n Gyro: Dnd, [2n,2+ ], (2*n), order 4n |
Rotation group | Dn, [n,2]+, (n22), order 2n |
Properties | convex |
Ingeometry, a birotunda is any member of a family of dihedral-symmetric polyhedra, formed from two rotunda adjoined through the largest face. They are similar to a bicupola but instead of alternating squares and triangles, it alternates pentagons and triangles around an axis. There are two forms, ortho- and gyro-: an orthobirotunda has one of the two rotundas is placed as the mirror reflection of the other, while in a gyrobirotunda one rotunda is twisted relative to the other.
The pentagonal birotundas can be formed with regular faces, one a Johnson solid, the other a semiregular polyhedron:
Other forms can be generated with dihedral symmetry and distorted equilateral pentagons.
4 | 5 | 6 | 7 | 8 |
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![]() square orthobirotunda |
![]() pentagonal orthobirotunda |
![]() hexagonal orthobirotunda |
![]() heptagonal orthobirotunda |
![]() octagonal orthobirotunda |
![]() square gyrobirotunda |
![]() pentagonal gyrobirotunda (icosidodecahedron) |
![]() hexagonal gyrobirotunda |
![]() heptagonal gyrobirotunda |
![]() octagonal gyrobirotunda |
Convex polyhedra
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Platonic solids (regular) |
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Catalan solids |
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Dihedral regular |
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Dihedral uniform |
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Dihedral others |
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Degenerate polyhedra are in italics. |