Petrial truncated tetrahedron
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Petrial truncated tetrahedron  

Rank  3 
Type  Noble, Scaliform, Orbiform 
Elements  
Faces  3 threeorbit skew dodecagons 
Edges  6+12 
Vertices  12 
Vertex figure  Isosceles triangle, edge lengths 1, , 
Measures (edge length 1)  
Circumradius  
Related polytopes  
Army  Tut 
Regiment  Tut 
Petrie dual  Truncated tetrahedron 
Convex hull  Truncated tetrahedron 
Abstract & topological properties  
Flag count  72 
Euler characteristic  3 
Orientable  No 
Genus  5 
Properties  
Symmetry  A_{3}, order 24 
Flag orbits  3 
The Petrial truncated tetrahedron is a noble skeletal polyhedron in 3dimensional space. It is vertex and face transitive as well as equilateral. It is one of 188 3orbit polyhedra of full rank with irreducible symmetry.
Vertex coordinates[edit  edit source]
The vertex coordinates of the Petrial truncated tetrahedron are the same as those of its Petrial.
Gallery[edit  edit source]

A single face of the Petrial truncated tetrahedron
References[edit  edit source]
 Cunningham, Gabe (2024), "Finite 3orbit 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