Birotunda

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Set of birotundas
Pentagonal orthobirotundaPentagonal gyrobirotunda
(Example Ortho/gyro pentagonal forms)
Faces 2 n-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

In geometry, 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.

See also[edit]

References[edit]

  • Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
  • Victor A. Zalgaller (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. No ISBN.  The first proof that there are only 92 Johnson solids.