# Triangular pyramid

Triangular pyramid Rank3
SpaceSpherical
Bowers style acronymTripy
Info
Coxeter diagramox3oo&#y
SymmetryA2×I, order 6
ArmyTripy
RegimentTripy
Elements
Vertex figures1 equilateral triangle
3 isosceles triangles
Faces1 equilateral triangle, 3 isosceles triangles
Edges3+3
Vertices1+3
Measures (edge lengths b [base], ℓ [lacing])
Circumradius$\frac{l}{2\sqrt{1-\frac{b^2}{3l^2}}}$ Volume$\frac{\sqrt3b^2}{12}\sqrt{l^2-\frac{b^2}{3}}$ Height$\sqrt{l^2-\frac{b^2}{3}}$ Central density1
Euler characteristic2
Related polytopes
DualTriangular pyramid
ConjugateTriangular pyramid
Properties
ConvexYes
OrientableYes
NatureTame

The triangular pyramid, or tripy, is a type of tetrahedron with 1 equilateral triangle as a base and 3 isosceles triangles as sides. It is a pyramid based on the equilateral triangle.

It generally has 2 edge sizes, the base and side edges.

## In vertex figures

Triangular pyramids occur as the vertex figures in 8 nonprismatic uniform polychora (including the truncated pentachoron, truncated tesseract, truncated icositetrachoron, truncated hecatonicosachoron, truncated great grand hecatonicosachoron, quasitruncated tesseract, quasitruncated small stellated hecatonicosachoron, and quasitruncated great grand stellated hecatonicosachoron) and 3 polyhedral prisms (the tetrahedral prism, dodecahedral prism, and great stellated dodecahedral prism).