Octahedron (EntityTopic, 14)
From Hi.gher. Space
(Difference between revisions)
m |
m |
||
| Line 11: | Line 11: | ||
| index=9 | | index=9 | ||
| bracket=<xyz> | | bracket=<xyz> | ||
| + | }}{{STS Polytope | ||
| + | | flayout={{FLD|a3|end|e4}} | ||
| + | | petrie=6,0 | ||
| + | | dual=[[Cube]] | ||
}}{{STS Uniform polytope | }}{{STS Uniform polytope | ||
| wythoff=<nowiki>4 | 2 3, 2 | 3 3, or | 2 2 3 |</nowiki> | | wythoff=<nowiki>4 | 2 3, 2 | 3 3, or | 2 2 3 |</nowiki> | ||
| Line 18: | Line 22: | ||
| bowers=Oct | | bowers=Oct | ||
| kana=ｵｸ | | kana=ｵｸ | ||
| - | |||
}}}} | }}}} | ||
Revision as of 11:03, 1 November 2009
Equations
- Variables:
l ⇒ length of edges of the octahedron
- The hypervolumes of a octahedron are given by:
total edge length = 12l
surface area = 2sqrt(3)l2
volume = sqrt(3)-1l3
- The planar cross-sections (n) of an octahedron are:
[!x, !y, !z] ⇒ square of side (sqrt(2)-1l-abs(n)) rotated by 45°
Segmentation
The octahedron of side √2 may be segmented into 8× irregular tetrahedron with sides 3×1, 3×22-1.
| 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 |
| 8. <[xy]z> Wide octahedron | 9. <xyz> Octahedron | 10. <(xy)z> Bicone |
| List of bracketopes | ||
