# Elongated bowtie tegum

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Elongated bowtie tegum
Rank3
TypeOrbiform
Notation
Bowers style acronymEbot
Elements
Faces4 triangles, 2 squares, 2 hexagons
Edges4+4+8
Vertices2+8
Vertex figures2 bowties, edge lengths 1 and 3
8 scalene triangles, edge lengths 1, 2, 3
Measures (edge length 1)
Volume${\displaystyle {\frac {2{\sqrt {2}}}{3}}\approx 0.94281}$
Dihedral angles3–4: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
3–6: ${\displaystyle \arccos \left({\frac {1}{3}}\right)\approx 70.52878^{\circ }}$
4–6: ${\displaystyle \arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }}$
Related polytopes
ArmyBidiminished Co
RegimentEbot
ConjugateNone
Abstract & topological properties
Flag count64
OrientableYes
Properties
SymmetryK3, order 8
ConvexNo
NatureTame

The elongated bowtie tegum, or ebot, is a nonconvex orbiform polyhedron and an edge-faceting of the cuboctahedron. Its faces are 4 triangles, 2 squares, and 2 hexagons.

## Vertex coordinates

The vertices of an elongated bowtie tegum of edge length 1 are given by:

• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {\sqrt {2}}{2}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{2}},\,0,\,\pm {\frac {\sqrt {2}}{2}}\right)}$,
• ${\displaystyle \pm \left(0,\,{\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}}\right)}$.

These are the vertices of a cuboctahedron with two opposite points removed.