Square antiprism (EntityTopic, 13)
From Hi.gher. Space
(Difference between revisions)
m |
(add incidence matrix) |
||
| (13 intermediate revisions not shown) | |||
| Line 1: | Line 1: | ||
| - | {{Shape|Square antiprism| | + | <[#ontology [kind topic] [cats 3D Uniform Polytope Antiprism]]> |
| - | + | {{STS Shape | |
| + | | name=Square antiprism | ||
| + | | image=<[#embed [hash 4MBHT41ZEEQ7GV9TMNXD41SKW4] [width 180]]> | ||
| + | | dim=3 | ||
| + | | elements=10, 16, 8 | ||
| + | | sym=[[Stauroantiprismatic symmetry|D<sub>4d</sub>]] | ||
| + | | genus=0 | ||
| + | | ssc=[xG8]A | ||
| + | | ssc2=G4$H4 | ||
| + | | extra= | ||
| + | {{STS Polytope | ||
| + | | flayout={{FLD|a4|i|ade|cr|e8}} | ||
| + | | dual=[[Tetragonal trapezohedron]] | ||
| + | }}{{STS Uniform polytope | ||
| + | | schlaefli=s{2,4} | ||
| + | | conway=A4 | ||
| + | | vfigure=[[Trapezium]] | ||
| + | | vlayout=[[Triangle|3]]<sup>3</sup>∙[[Square|4]] | ||
| + | }}}} | ||
The '''square antiprism''' is a special case of an [[antiprism]] where the base is a [[square]]. | The '''square antiprism''' is a special case of an [[antiprism]] where the base is a [[square]]. | ||
| - | == | + | == Cross-sections == |
| + | *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 irregular [[pentagon]]s, degenerating to [[trapezium]]s in the middle and at the ends. | ||
| - | + | <[#polytope [id 93]]> | |
| - | + | ||
{{Polyhedra}} | {{Polyhedra}} | ||
| - | |||
| - | |||
Latest revision as of 23:00, 14 March 2014
The square antiprism is a special case of an antiprism where the base is a square.
Cross-sections
- 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.
Incidence matrix
Dual: tetragonal trapezohedron
| # | TXID | Va | Ea | Eb | 4a | 3a | Type | Name |
|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | |||||
| 1 | Ea | 2 | = digon | ; | ||||
| 2 | Eb | 2 | = digon | ; | ||||
| 3 | 4a | 4 | 4 | 0 | = square | ; | ||
| 4 | 3a | 3 | 1 | 2 | = triangle | ; | ||
| 5 | C1a | 8 | 8 | 8 | 2 | 8 | = square antiprism | ; |
Usage as facets
- 2× 1-facets of a square biantiprismatic ring
| 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 |
