Acronym  so 
Name 
stella octangula, 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  [3^{3}] 
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
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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