Английская Википедия:Elongated bipyramid
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Шаблон:Short description Шаблон:Infobox polyhedron
In geometry, the elongated bipyramids are an infinite set of polyhedra, constructed by elongating an Шаблон:Nowrap bipyramid (by inserting an Шаблон:Nowrap prism between its congruent halves).
There are three elongated bipyramids that are Johnson solids:
- Elongated triangular bipyramid (Шаблон:Math),
- Elongated square bipyramid (Шаблон:Math), and
- Elongated pentagonal bipyramid (Шаблон:Math).
Higher forms can be constructed with isosceles triangles.
Forms
| Name | elongated triangular bipyramid Шаблон:Math |
elongated square bipyramid Шаблон:Math |
elongated pentagonal bipyramid Шаблон:Math |
elongated hexagonal bipyramid |
|---|---|---|---|---|
| Type | Equilateral | Irregular | ||
| Image | Файл:Elongated triangular dipyramid.png | Файл:Elongated square dipyramid.png | Файл:Elongated pentagonal dipyramid.png | Файл:Elongated hexagonal dipyramid.png |
| Faces | 6 triangles, 3 squares |
8 triangles, 4 squares |
10 triangles, 5 squares |
12 triangles, 6 squares |
| Dual | triangular bifrustum | square bifrustum | pentagonal bifrustum | hexagonal bifrustum |
Applications
Elongated bipyramids are sometimes used as dice, especially to make dice with atypical side count, such as 5 or 7. Such a die has numbers written on the square faces, which are usually heightened into rectangles for convenience in rolling. Whichever number comes face-up when the die is rolled is the side that is to be read.
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.
