Bowtie tegum

Bowtie tegum
(3D model) (OFF file)
Rank	3
Type	Orbiform
Space	Spherical
Notation
Bowers style acronym	Bobipyr
Elements
Faces	4 triangles, 2 squares
Edges	2+8
Vertices	2+4
Vertex figures	2 bowties, edge lengths 1, √2
	4 isosceles triangles, edge lengths 1, 1, √2
Measures (edge length 1)
Circumradius	$\frac{\sqrt2}2 \approx 0.70711$
Dihedral angles	3-3: $\arccos\left(-\frac13\right) \approx 109.47122^\circ$
	3-4: $\arccos\left(\frac{\sqrt3}3\right) \approx 54.73561^\circ$
Related polytopes
Army	Oct
Dual	Bowtie tegum (abstract)
Conjugate	None
Abstract & topological properties
Flag count	40
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	K3, order 8
Convex	No
Nature	Tame

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.

External links

• Bowers, Jonathan. "Batch 1: Oct and Co Facetings" (#4 under oct).

• Klitzing, Richard. "bobipyr".