Octahedron (EntityTopic, 14)
From Hi.gher. Space
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The octahedron of side √2 may be [[segment]]ed into 8× irregular [[tetrahedron]] with sides 3×1, 3×2<sup>2<sup>-1</sup></sup>. | The octahedron of side √2 may be [[segment]]ed into 8× irregular [[tetrahedron]] with sides 3×1, 3×2<sup>2<sup>-1</sup></sup>. | ||
| - | {{Cross polytopes}} | + | {{Cross polytopes|3}} |
{{Trishapes}} | {{Trishapes}} | ||
{{Bracketope Nav|8|9|10|<[xy]z><br>Wide octahedron|<xyz><br>Octahedron|<(xy)z><br>Bicone|hedra}} | {{Bracketope Nav|8|9|10|<[xy]z><br>Wide octahedron|<xyz><br>Octahedron|<(xy)z><br>Bicone|hedra}} | ||
[[Category:Regular polyhedra]] | [[Category:Regular polyhedra]] | ||
Revision as of 17:16, 30 May 2010
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.
| Cross polytopes |
| diamond • octahedron • aerochoron • aeroteron • aeropeton |
| 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 | ||
