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)	between {3} and {3}:   arccos(1/3) = 70.528779°
Confer	related compounds: sis   general polytopal classes: regular
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