Acronym | so |
Name |
stella octangula, star tetrahedron, compound of 2 tet |
Coxeter symbol | {4,3}[2{3,3}]{3,4} |
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Circumradius | sqrt(3/8) = 0.612372 |
Inradius | 1/sqrt(24) = 0.204124 |
Vertex figure | [33] |
General of army | cube |
Colonel of regiment | (is itself locally convex) |
Admiral of fleet | oct |
Dual | selfdual |
Dihedral angles
(at margins) |
|
Confer | |
External links |
Aside: In projective space even a third tetrahedron could be added such, that the edges all intersect by three. In fact one vertex then would be at the center and the others at the plane of infinity. This configuration then is known as the desmic tetrahedra: a representation of a desmic configuration of 3 sets of points (here: the vertices of either tetrahedron), where any line through 2 points from 2 of these sets also passes through a point of the third set.
Incidence matrix according to Dynkin symbol
xo4/2ox&#x → height = 1/sqrt(2) = 0.707107 o.4/2o. & | 8 | 1 2 | 3 -------------+---+-----+-- x. .. & | 2 | 4 * | 2 oo4/2oo&#x | 2 | * 8 | 2 -------------+---+-----+-- xo ..&#x & | 3 | 1 2 | 8
xo3oo3ox o.3o.3o. & | 8 | 3 | 3 || 1 ------------+---+----+---++-- x. .. .. & | 2 | 12 | 2 || 1 ------------+---+----+---++-- x.3o. .. & | 3 | 3 | 8 || 1 ------------+---+----+---++-- x.3o.3o. & ♦ 4 | 6 | 4 || 2
o3o4β both( . . . ) | 8 | 3 | 3 || 1 --------------+---+----+---++-- both( . o4s ) | 2 | 12 | 2 || 1 --------------+---+----+---++-- sefa( o3o4β ) | 3 | 3 | 8 || 1 --------------+---+----+---++-- both( o3o4s ) ♦ 4 | 6 | 4 || 2 starting figure: o3o4x
β2o4β both( . . . ) | 8 | 2 1 | 3 || 1 --------------+---+-----+---++-- both( s 2 s ) | 2 | 8 * | 2 || 1 both( . o4s ) | 2 | * 4 | 2 || 1 --------------+---+-----+---++-- sefa( β2o4β ) | 3 | 2 1 | 8 || 1 --------------+---+-----+---++-- both( s2o4s ) ♦ 4 | 4 2 | 4 || 2 starting figure: x o4x
β2β2β both( . . . ) | 8 | 1 1 1 | 3 || 1 --------------+---+-------+---++-- both( s2s . ) | 2 | 4 * * | 2 || 1 both( s 2 s ) | 2 | * 4 * | 2 || 1 both( . s2s ) | 2 | * * 4 | 2 || 1 --------------+---+-------+---++-- sefa( β2β2β ) | 3 | 1 1 1 | 8 || 1 --------------+---+-------+---++-- both( s2s2s ) ♦ 4 | 2 2 2 | 4 || 2 starting figure: x x x
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