# Elongated triangular pyramid

Elongated triangular pyramid
Rank3
TypeCRF
Notation
Bowers style acronymEtripy
Coxeter diagramoxx3ooo&#xt
Elements
Faces
Edges3+3+3+3
Vertices1+3+3
Vertex figures1 triangle, edge length 1
3 kites, edge lengths 1 and 2
3 isosceles triangles, edge lengths 1, 2, 2
Measures (edge length 1)
Volume${\displaystyle {\frac {{\sqrt {2}}+3{\sqrt {3}}}{12}}\approx 0.55086}$
Dihedral angles3–4 join: ${\displaystyle \arccos \left(-{\frac {2{\sqrt {2}}}{3}}\right)\approx 160.52878^{\circ }}$
3–4 prismatic: 90°
3–3: ${\displaystyle \arccos \left({\frac {1}{3}}\right)\approx 70.52878^{\circ }}$
4–4: 60°
Central density1
Number of external pieces7
Level of complexity8
Related polytopes
ArmyEtripy
RegimentEtripy
DualElongated triangular pyramid
ConjugateNone
Abstract & topological properties
Flag count48
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA2×I, order 6
Flag orbits8
ConvexYes
NatureTame

The elongated triangular pyramid (OBSA: etripy) is one of the 92 Johnson solids (J7). It consists of 1+3 triangles and 3 squares. It can be constructed by attaching a triangular prism to one of the faces of the tetrahedron, seen as a triangular pyramid.

If a second tetrahedron is attached to the other triangular base of the prism, the result is the elongated triangular bipyramid.

## Vertex coordinates

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

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