Blend of 2 triangular prisms

Blend of 2 triangular prisms
(OFF file)
Rank	3
Type	Segmentotope
Notation
Bowers style acronym	Tutrip
Elements
Faces	4 triangles, 4 squares
Edges	2+4+8
Vertices	4+4
Vertex figures	4 isosceles triangles, edge lengths 1, √2, √2
	4 butterflies, edge lengths 1 and √2
Measures (edge length 1)
Circumradius	${\frac {\sqrt {21}}{6}}\approx 0.76376$
Volume	$0$
Dihedral angles	3-4 (trip edges): 90°
	4–4: 60°
	3-4 (at pseudo {4}): 30°
Height	Stellated square atop pseudo square: ${\frac {\sqrt {3}}{2}}\approx 0.86603$
Army	Square antipodium
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	B2×I, order 8
Convex	No
Nature	Tame

The blend of 2 triangular prisms, or tutrip, is a segmentohedron. It consists of 4 triangles and 4 squares. It is a cupolaic blend of two triangular prisms seen as digonal cupolae sharing a square face which blends out.

It is a segmentohedron as a stellated square (a degenerate compound of 2 perpendicular edges) atop pseudo square. It is notable for showing up as a cell in many scaliform polytopes, and is one of the simplest orbiform polyhedra that can be constructed only as a blend, rather than by removing vertices from a larger polyhedron.

It is isomorphic to the gyrobifastigium.

It has multiple analogues in higher dimensions, such as the blend of 3 square pyramidal prisms and blend of 3 triangular-square duoprisms in 4D.

It is the 4-4-3 acrohedron generated by Green's rules.

Vertex coordinates

A tutrip of edge length 1 has vertex coordinates given by:

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

External links

• Klitzing, Richard. "tutrip".