# Biaugmented triangular prism

Biaugmented triangular prism Rank3
TypeCRF
SpaceSpherical
Notation
Bowers style acronymBautip
Elements
Faces2+2+2+4 triangles, 1 square
Edges1+2+2+4+4+4
Vertices2+2+4
Vertex figures2 squares, edge length 1
4 trapezoids, edge lengths 1, 1, 1, 2
2 pentagons, edge length 1
Measures (edge length 1)
Volume$\frac{4\sqrt2+3\sqrt3}{12} ≈ 0.90442$ Dihedral angles3–3 double join: $\arccos\left(-\frac{1+2\sqrt6}{6}\right) ≈ 169.47122^\circ$ 3–3 single join: $\arccos\left(-\frac{\sqrt6}{3}\right) ≈ 144.73561^\circ$ 3–4 join: $\arccos\left(-\frac{3\sqrt2-\sqrt3}{6}\right) ≈ 114.73561^\circ$ 3–3 pyramidal: $\arccos\left(-\frac13\right) ≈ 109.47122^\circ$ 3–4 prismatic: 90°
Central density1
Related polytopes
ArmyBautip
RegimentBautip
DualLaterobitruncated triangular tegum
ConjugateBiaugmented triangular prism
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryK2×I, order 4
ConvexYes
NatureTame

The biaugmented triangular prism is one of the 92 Johnson solids (J50). It consists of 2+2+2+4 triangles and 1 square. It can be constructed by attaching square pyramids to two of the square faces of the triangular prism.

## Vertex coordinates

A biaugmented triangular prism of edge length 1 has the following vertices:

• $\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12\right),$ • $\left(0,\,\frac{\sqrt3}{3},\,±\frac12\right),$ • $\left(±\frac{1+\sqrt6}{4},\,\frac{3\sqrt2+\sqrt3}{12},\,0\right).$ ## In vertex figures

Variants of the biaugmented triangular prism (in its symmetry axis, with non-base connected edge lengths of 2) by changing the edge opposite to the square appear as the vertex figure of the nonuniform antiditetragoltriate, and has no corealmic realization.