小星形十二面體
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在幾何學上，小星形十二面體是克卜勒－龐索立體。 It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.
The 12 vertices match the locations for an icosahedron. The 30 edges are shared by the great icosahedron.
It is considered the first of three stellations of the dodecahedron.
If the pentagrammic faces are considered as 5 triangular faces, it shares the same surface topology as the pentakis dodecahedron, but with much taller isosceles triangle faces.
| 小星形十二面體 | |
|---|---|
 (按這裡觀看旋轉模型) |
|
| 類別 | 克卜勒－龐索立體 |
| 歐拉特徵數 | F=12, E=30, V=12 (χ=-6) |
| Faces by sides | 12{5/2} |
| 施萊夫利符號 | {5/2,5} |
| Wythoff symbol | 5 | 25/2 |
| 對稱群 | Ih |
| Index references | U34, C43, W20 |
| 對偶 | 大十二面體 |
| 特性 | 正凹多面體 |
| 二面角 | 116.56° = π − arctan(2) |
 頂點圖 (5/2)5 |
|
Image:Gravitation.png
Small Stellated dodecahedron
Gravitation (M. C. Escher)
Gravitation (M. C. Escher)
A transparent model of the small stellated dodecahedron (See also Animated)
[编辑] As a stellation
It can also be constructed as the first of four stellations of the dodecahedron, and referenced as Wenninger model [W20].
The stellation facets for construction are:
[编辑] References
- Wenninger，Magnus (1974). Polyhedron Models，Cambridge University Press. ISBN 0-521-09859-9.
- Coxeter，H. S. M. (1938). The Fifty-Nine Icosahedra，Springer-Verlag, New York, Berlin, Heidelberg. ISBN 0-387-90770-X.
[编辑] External links
- MathWorld: Small stellated dodecahedron
- MathWorld: Three stellations of the dodecahedronTemplate:Polyhedron-stub
