# Bowtie tegum

(Redirected from Bobipyr)
Bowtie tegum
Rank3
TypeOrbiform
Notation
Bowers style acronymBobipyr
Elements
Faces4 triangles, 2 squares
Edges2+8
Vertices2+4
Vertex figures2 bowties, edge lengths 1, 2
4 isosceles triangles, edge lengths 1, 1, 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Dihedral angles3-3: ${\displaystyle \arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }}$
3-4: ${\displaystyle \arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }}$
Related polytopes
ArmyOct
DualBowtie tegum (abstract)
ConjugateNone
Abstract & topological properties
Flag count40
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryK3, order 8
ConvexNo
NatureTame

The bowtie tegum, also called the bowtie bipyramid or bobipyr, is an orbiform polyhedron. It is an edge-faceting of the octahedron, using 4 of its triangles and 2 of the central squares of the tetrahemihexahedron. The abstract bowtie tegum would have two pairs of triangles which in this polyhedron merge into squares.

This polyhedron is abstractly self-dual.

It appears as a cell in some scaliform polychora of the hexadecachoron regiment: the skew octahemioctachoron, the hemitesseractihemioctachoron, and the sesquitesseractihemioctachoron.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the octahedron.