Acronym	bobipyr
Name	bowtie bipyramid, crossed-square bipyramid, bowtie (line-)tegum
Circumradius	1/sqrt(2) = 0.707107
General of army	oct
Dihedral angles	between {3} and {3}:   arccos(-1/3) = 109.471221° between {3} and {4}:   arccos[1/sqrt(3)] = 54.735610°
Face vector	6, 10, 6
Confer	uniform relative: oct   thah   related Johnson solids: squippy
External links

This non-convex scaliform polyhedron is an only briquet symmetrical ridge-faceting of the oct. In fact, similar as thah is derived by all 3 internal squares and squippy by only 1 internal square, bobipyr is obtained by using 2 internal squares instead.

The second incidence matrix below shows that bobipyr, taken as an abstract polyhedron, would be self-dual.

Incidence matrix according to Dynkin symbol

oxo(-x)&#xr

o...     & | 2 * | 4 0 | 2 2
.o..     & | * 4 | 2 1 | 2 1
-----------+-----+-----+----
oo..&#x  & | 1 1 | 8 * | 1 1
.x..     & | 0 2 | * 2 | 2 0
-----------+-----+-----+----
ox..&#x  & | 1 2 | 2 1 | 4 *
oooo&#xr   | 2 2 | 4 0 | * 2

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