Английская Википедия:Elongated cupola
Материал из Онлайн справочника
| Set of elongated cupolae | |
|---|---|
| Файл:Elongated pentagonal cupola.png Example pentagonal form | |
| Faces | n triangles 3n squares 1 n-gon 1 2n-gon |
| Edges | 9n |
| Vertices | 5n |
| Symmetry group | Cnv, [n], (*nn) |
| Rotational group | Cn, [n]+, (nn) |
| Dual polyhedron | |
| Properties | convex |
In geometry, the elongated cupolae are an infinite set of polyhedra, constructed by adjoining an n-gonal cupola to an 2n-gonal prism.
There are three elongated cupolae that are Johnson solids made from regular triangles and square, and pentagons. Higher forms can be constructed with isosceles triangles. Adjoining a triangular prism to a cube also generates a polyhedron, but has adjacent parallel faces, so is not a Johnson solid. Higher forms can be constructed without regular faces.
Forms
| name | faces | |
|---|---|---|
| Файл:Elongated digonal cupola.png | elongated digonal cupola | 2 triangles, 6+1 squares |
| Файл:Elongated triangular cupola.png | elongated triangular cupola (J18) | 3+1 triangles, 9 squares, 1 hexagon |
| Файл:Elongated square cupola.png | elongated square cupola (J19) | 4 triangles, 12+1 squares, 1 octagon |
| Файл:Elongated pentagonal cupola.png | elongated pentagonal cupola (J20) | 5 triangles, 15 squares, 1 pentagon, 1 decagon |
| elongated hexagonal cupola | 6 triangles, 18 squares, 1 hexagon, 1 dodecagon |
See also
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.
- Шаблон:Cite book The first proof that there are only 92 Johnson solids.
