Blend of 2 triangular prisms

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Blend of 2 triangular prisms
Rank3
TypeSegmentotope
Notation
Bowers style acronymTutrip
Elements
Faces4 triangles, 4 squares
Edges2+4+8
Vertices4+4
Vertex figures4 isosceles triangles, edge lengths 1, 2, 2
4 butterflies, edge lengths 1 and 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {21}}{6}}\approx 0.76376}$
Volume${\displaystyle 0}$
Dihedral angles3-4 (trip edges): 90°
4–4: 60°
3-4 (at pseudo {4}): 30°
HeightStellated square atop pseudo square: ${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Related polytopes
ArmySquare antipodium
Abstract & topological properties
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryB2×I, order 8
ConvexNo
NatureTame

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:

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