Elongated triangular pyramid

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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
Dihedral angles3–4 join:
 3–4 prismatic: 90°
 3–3:
 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[edit | edit source]

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

  • ,
  • ,
  • .

External links[edit | edit source]