Square antiprism (EntityTopic, 13)
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== Geometry == | == Geometry == | ||
| - | * The [[planar]] [[cross-section]]s of a square antiprism in the [!z] plane are | + | * The [[planar]] [[cross-section]]s of a square antiprism in the [!z] plane are [[octagon]]s, giving a regular octagon in the middle and degenerating to squares at the ends. |
| - | * The planar cross-sections of a square antiprism in the [!x] and [!y] planes are [[trapezium]]s. | + | * The planar cross-sections of a square antiprism in the [!x] and [!y] planes are irregular [[pentagon]]s, degenerating to [[trapezium]]s in the middle and at the ends. |
{{Polyhedra}} | {{Polyhedra}} | ||
[[Category:Trishapes]] | [[Category:Trishapes]] | ||
Revision as of 10:47, 5 December 2010
The square antiprism is a special case of an antiprism where the base is a square.
Geometry
- The planar cross-sections of a square antiprism in the [!z] plane are octagons, giving a regular octagon in the middle and degenerating to squares at the ends.
- The planar cross-sections of a square antiprism in the [!x] and [!y] planes are irregular pentagons, degenerating to trapeziums in the middle and at the ends.
| Notable Trishapes | |
| Regular: | tetrahedron • cube • octahedron • dodecahedron • icosahedron |
| Direct truncates: | tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate |
| Mesotruncates: | stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron |
| Snubs: | snub staurohedron • snub rhodohedron |
| Curved: | sphere • torus • cylinder • cone • frustum • crind |
