Acronym  bobipyr 
Name 
bowtie bipyramid, crossed tetragonal bipyramid, bowtie (line)tegum 
Circumradius  1/sqrt(2) = 0.707107 
General of army  oct 
Dihedral angles 

Confer 

This nonconvex scaliform polyhedron is an only briquet symmetrical ridgefaceting of the oct. In fact, just as thah is derived by all 3 internal squares and squippy by only 1 internal square, bobipyr is obtained by 2 internal squares.
The second incidence matrix below shows that bobipyr, taken as an abstract polyhedron, would be selfdual.
pt  xq(x)q  pt → height = 1/sqrt(2) = 0.707107 1 * *  4 0 0  2 2 0 * 4 *  1 1 1  1 1 1 * * 1  0 0 4  0 2 2 ++ 1 1 0  4 * *  1 1 0 0 2 0  * 2 *  1 0 1 0 1 1  * * 4  0 1 1 ++ 1 2 0  2 1 0  2 * * 1 2 1  2 0 2  * 2 * 0 2 1  0 1 2  * * 2
or 2 *  4 0  2 2 * 4  2 1  2 1 ++ 1 1  8 *  1 1 0 2  * 2  2 0 ++ 1 2  2 1  4 * 2 2  4 0  * 2
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