Bicupola
In geometry, a bicupola is a solid formed by connecting two cupolae on their bases. Here, two classes of bicupola are included because each cupola (bicupola half) is bordered by alternating triangles and squares. If similar faces are attached together the result is an orthobicupola; if squares are attached to triangles it is a gyrobicupola.
Forms
[edit]In the first column of the two following tables, the symbols are Schoenflies, Coxeter, and orbifold notation, in this order.
Set of orthobicupolae
[edit]| Symmetry | Picture | Description |
|---|---|---|
| D3h [2,3] *223 |
 |
Triangular orthobicupola (J27): 8 triangles, 6 squares.[1][2] Its dual is the trapezo-rhombic dodecahedron |
| D4h [2,4] *224 |
 |
Square orthobicupola (J28): 8 triangles, 10 squares.[2] |
| D5h [2,5] *225 |
 |
Pentagonal orthobicupola (J30): 10 triangles, 10 squares, 2 pentagons.[2] |
| Dnh [2,n] *22n |
n-gonal orthobicupola: 2n triangles, 2n rectangles, 2 n-gons |
Set of gyrobicupolae
[edit]An n-gonal gyrobicupola has the same topology as an n-gonal rectified antiprism, Conway polyhedron notation: aAn.[clarification needed]
| Symmetry | Picture | Description |
|---|---|---|
| D2d [2+,4] 2*2 |
 |
Gyrobifastigium (J26) or digonal gyrobicupola: 4 triangles, 4 squares.[3] |
| D3d [2+,6] 2*3 |
 |
Triangular gyrobicupola or cuboctahedron: 8 triangles, 6 squares.[1][2] Its dual is the rhombic dodecahedron. |
| D4d [2+,8] 2*4 |
 |
Square gyrobicupola (J29): 8 triangles, 10 squares.[2] Its dual is the elongated tetragonal trapezohedron |
| D5d [2+,10] 2*5 |
 |
Pentagonal gyrobicupola (J31): 10 triangles, 10 squares, 2 pentagons.[2] Its dual is the elongated pentagonal trapezohedron |
| Dnd [2+,2n] 2*n |
n-gonal gyrobicupola: 2n triangles, 2n rectangles, 2 n-gons. |
See also
[edit]References
[edit]- 1 2 Ogievetsky, O.; Shlosman, S. (2021). "Platonic compounds and cylinders". In Novikov, S.; Krichever, I.; Ogievetsky, O.; Shlosman, S. (eds.). Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry. American Mathematical Society. p. 477. ISBN 978-1-4704-5592-7.
- 1 2 3 4 5 6 Berman, M. (1971). "Regular-faced convex polyhedra". Journal of the Franklin Institute. 291 (5): 329–352. doi:10.1016/0016-0032(71)90071-8. MR 0290245.
- ↑ Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/CJM-1966-021-8. MR 0185507. S2CID 122006114.; Table III, line 26