# Elongated triangular orthobicupola

Elongated triangular orthobicupola
Rank3
TypeCRF
Notation
Bowers style acronymEtobcu
Coxeter diagramoxxo3xxxx&#xt
Elements
Faces
Edges6+6+6+6+12
Vertices6+12
Vertex figures6 rectangles, edge lengths 1 and 2
12 trapezoids, edge lengths 1, 2, 2, 2
Measures (edge length 1)
Volume${\displaystyle {\frac {10{\sqrt {2}}+9{\sqrt {3}}}{6}}\approx 4.95510}$
Dihedral angles3–4 join: ${\displaystyle \arccos \left(-{\frac {2{\sqrt {2}}}{3}}\right)\approx 160.52878^{\circ }}$
4–4 join: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }}$
3–4 cupolaic: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
4–4 prismatic: 120°
Central density1
Number of external pieces20
Level of complexity12
Related polytopes
ArmyEtobcu
RegimentEtobcu
ConjugateNone
Abstract & topological properties
Flag count144
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA2×A1, order 12
Flag orbits12
ConvexYes
NatureTame

The elongated triangular orthobicupola (OBSA: etobcu) is one of the 92 Johnson solids (J35). It consists of 2+6 triangles and 3+3+6 squares. It can be constructed by inserting a hexagonal prism between the two halves of the triangular orthobicupola.

## Vertex coordinates

An elongated triangular orthobicupola of edge length 1 has the following vertices:

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