# Elongated triangular bipyramid

Elongated triangular bipyramid
Rank3
TypeCRF
Notation
Bowers style acronymEtidpy
Coxeter diagramoxxo3ooo&#xt
Elements
Faces
Edges3+6+6
Vertices2+6
Vertex figures2 triangles, edge length 1
3 kites, edge lengths 1 and 2
Measures (edge length 1)
Volume${\displaystyle {\frac {2{\sqrt {2}}+3{\sqrt {3}}}{12}}\approx 0.66871}$
Dihedral angles3–4: ${\displaystyle \arccos \left(-{\frac {2{\sqrt {3}}}{3}}\right)\approx 160.52878^{\circ }}$
3–3: ${\displaystyle \arccos \left({\frac {1}{3}}\right)\approx 70.52878^{\circ }}$
4–4: 60°
Central density1
Number of external pieces9
Level of complexity5
Related polytopes
ArmyEtidpy
RegimentEtidpy
DualTriangular bifrustum
ConjugateNone
Abstract & topological properties
Flag count60
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA2×A1, order 12
Flag orbits5
ConvexYes
NatureTame

The elongated triangular bipyramid (OBSA: etidpy) is one of the 92 Johnson solids (J14). It consists of 6 triangles and 3 squares. It can be constructed by inserting a triangular prism between the two halves of the triangular bipyramid.

## Vertex coordinates

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

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