Rotunda (geometry)

Short description: Solid made by joining an n- and 2n-gon with triangles and pentagons

Set of rotundas

(Example: pentagonal rotunda)

Faces| 1 n-gon
1 2n-gon
n pentagons
2n triangles
Edges| 7n
Vertices| 4n
Symmetry group| Cnv, [n], (*nn), order 2n
Rotation group| Cn, [n]+, (nn), order n
Properties| convex

In geometry, a rotunda is any member of a family of dihedral-symmetric polyhedra. They are similar to a cupola but instead of alternating squares and triangles, it alternates pentagons and triangles around an axis. The pentagonal rotunda is a Johnson solid.

Other forms can be generated with dihedral symmetry and distorted equilateral pentagons. [example needed]

## Contents

* 1 Examples
* 2 Star-rotunda
* 3 See also
* 4 References

## Examples

Rotundas  3  | 4  | 5  | 6  | 7  | 8

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triangular rotunda  |
square rotunda  |
pentagonal rotunda |
hexagonal rotunda  |
heptagonal rotunda  |
octagonal rotunda

## Star-rotunda

Star-rotundas  5  | 7  | 9  | 11

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Pentagrammic rotunda  |
Heptagrammic rotunda  |
Enneagrammic rotunda  |
Hendecagrammic rotunda

## See also

* Birotunda

## References

* 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.

* v
* t
* e

Convex polyhedra

Platonic solids (regular)|

* tetrahedron
* cube
* octahedron
* dodecahedron
* icosahedron

Archimedean solids
(semiregular or uniform)

* truncated tetrahedron
* cuboctahedron
* truncated cube
* truncated octahedron
* rhombicuboctahedron
* truncated cuboctahedron
* snub cube
* icosidodecahedron
* truncated dodecahedron
* truncated icosahedron
* rhombicosidodecahedron
* truncated icosidodecahedron
* snub dodecahedron

Catalan solids
(duals of Archimedean)

* triakis tetrahedron
* rhombic dodecahedron
* triakis octahedron
* tetrakis hexahedron
* deltoidal icositetrahedron
* disdyakis dodecahedron
* pentagonal icositetrahedron
* rhombic triacontahedron
* triakis icosahedron
* pentakis dodecahedron
* deltoidal hexecontahedron
* disdyakis triacontahedron
* pentagonal hexecontahedron

Dihedral regular|

* dihedron
* hosohedron

Dihedral uniform|

* prisms
* antiprisms

duals:|

* bipyramids
* trapezohedra

Dihedral others|

* pyramids
* truncated trapezohedra
* gyroelongated bipyramid
* cupola
* bicupola
* pyramidal frusta
* bifrustum
* rotunda
* birotunda
* prismatoid
* scutoid

Degenerate polyhedra are in italics.

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