Biaugmented triangular prism

Biaugmented triangular prism
(3D model) (OFF file)
Rank	3
Type	CRF
Space	Spherical
Notation
Bowers style acronym	Bautip
Elements
Faces	2+2+2+4 triangles, 1 square
Edges	1+2+2+4+4+4
Vertices	2+2+4
Vertex figures	2 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 angles	3–3 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 density	1
Related polytopes
Army	Bautip
Regiment	Bautip
Dual	Laterobitruncated triangular tegum
Conjugate	Biaugmented triangular prism
Abstract & topological properties
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	K2×I, order 4
Convex	Yes
Nature	Tame

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.

External links

• Klitzing, Richard. "bautip".

• Quickfur. "The Biaugmented Triangular Prism".

• Wikipedia Contributors. "Biaugmented triangular prism".
• McCooey, David. "Biaugmented Triangular Prism"