Petrial truncated tetrahedron

Petrial truncated tetrahedron
Rank3
TypeNoble, Scaliform, Orbiform
Elements
Faces3 three-orbit skew dodecagons
Edges6+12
Vertices12
Vertex figureIsosceles triangle, edge lengths 1, ${\displaystyle {\sqrt {3}}}$, ${\displaystyle {\sqrt {3}}}$
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {22}}{4}}\approx 1.17260}$
Related polytopes
ArmyTut
RegimentTut
Petrie dualTruncated tetrahedron
Convex hullTruncated tetrahedron
Abstract & topological properties
Flag count72
Euler characteristic-3
OrientableNo
Genus5
Properties
SymmetryA3, order 24
Flag orbits3

The Petrial truncated tetrahedron is a noble skeletal polyhedron in 3-dimensional space. It is vertex and face transitive as well as equilateral. It is one of 188 3-orbit polyhedra of full rank with irreducible symmetry.

Vertex coordinates

The vertex coordinates of the Petrial truncated tetrahedron are the same as those of its Petrial.

References

• Cunningham, Gabe (2024), "Finite 3-orbit polyhedra in ordinary space, II", Boletín de la Sociedad Matemática Mexicana, 30
• Deza, Michel; Mathieu, Dutour (2004), Zigzag structure of complexes, arXiv:math/0405279
• Deza, Michel (2011), "Note on Petrie duals and hypercube embeddings of semiregular polyhedra", Symmetry: Culture and Science, 22: 263–267