Square antiprism
From Wikipedia, the free encyclopedia
| Uniform Square antiprism | |
|---|---|
 |
|
| Type | Prismatic uniform polyhedron |
| Elements | F = 10, E = 16 V = 8 (χ = 2) |
| Faces by sides | 8{3}+2{4} |
| Schläfli symbol | s{2,4} |
| Wythoff symbol | | 2 2 4 |
| Coxeter-Dynkin |    |
| Symmetry | D4d |
| References | U77(b) |
| Dual | Tetragonal trapezohedron |
| Properties | convex |
 Vertex figure 3.3.3.4 |
|
In geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.
If all its faces are regular, it is a semiregular polyhedron.
When eight points are distributed on the surface of a sphere with the aim of maximising the distance between them in some sense, then the resulting shape corresponds to a square anti-prism rather than a cube. Different examples include maximising the distance to the nearest point, or using electrons to maximise the sum of all reciprocals of squares of distances.
[edit] See also
- Compound of three square antiprisms
- Set of antiprisms
- Octahedron Triangle-capped antiprism
- Pentagonal antiprism
- Hexagonal antiprism
- Octagonal antiprism
[edit] External links
- Eric W. Weisstein, Antiprism at MathWorld.
- Square Antiprism interactive model
- Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra
- VRML model
- Conway Notation for Polyhedra Try: "A4"
