Octahedron (EntityTopic, 14)
From Hi.gher. Space
(Difference between revisions)
m |
|||
| Line 23: | Line 23: | ||
| kana=ｵｸ | | kana=ｵｸ | ||
}}}} | }}}} | ||
| + | |||
| + | The '''octahedron''' is a [[regular polyhedron]] with four [[triangle]]s around each vertex. However, it can be alternatively constructed as the [[mesotruncate]]d [[tetrahedron]], so it is also in the sequence of mesotruncated [[simplices]]. In addition, it is the central vertex-first [[cross-section]] of the [[tesseract]]. | ||
== Equations == | == Equations == | ||
Revision as of 21:16, 18 December 2010
The octahedron is a regular polyhedron with four triangles around each vertex. However, it can be alternatively constructed as the mesotruncated tetrahedron, so it is also in the sequence of mesotruncated simplices. In addition, it is the central vertex-first cross-section of the tesseract.
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 | ||
