# Metabiaugmented hexagonal prism

Metabiaugmented hexagonal prism
Rank3
TypeCRF
Notation
Bowers style acronymMabauhip
Elements
Faces
Edges2+2+2+2+2+4+4+4+4
Vertices2+4+4+4
Vertex figures2 squares, edge length 1
4+4 irregular tetragons, edge lengths 1, 1, 2, 3
4 isosceles triangles, edge lengths (1+5)/2, 2, 2
Measures (edge length 1)
Volume${\displaystyle {\frac {2{\sqrt {2}}+9{\sqrt {3}}}{6}}\approx 3.06948}$
Dihedral angles3–4: ${\displaystyle \arccos \left(-{\sqrt {\frac {7+2{\sqrt {6}}}{12}}}\right)\approx 174.73561^{\circ }}$
3–6: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }}$
4–4: 120°
3–3: ${\displaystyle \arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }}$
4–6: 90°
Central density1
Number of external pieces14
Level of complexity26
Related polytopes
ArmyMabauhip
RegimentMabauhip
DualMetalaterobitruncated hexagonal tegum
ConjugateMetabiaugmented hexagonal prism
Abstract & topological properties
Flag count104
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryK2×I, order 4
Flag orbits26
ConvexYes
NatureTame

The metabiaugmented hexagonal prism (OBSA: mabauhip) is one of the 92 Johnson solids (J56). It consists of 2+2+4 triangles, 1+1+2 squares, and 2 hexagons. It can be constructed by attaching square pyramids to two non-opposite, non-adjacent square faces of the hexagonal prism.

## Vertex coordinates

A metabiaugmented hexagonal prism of edge length 1 has the following vertices:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm 1,\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {3+{\sqrt {6}}}{4}},\,\pm {\frac {{\sqrt {2}}+{\sqrt {3}}}{4}},\,0\right)}$.