Petrie Expanded Truncated Polyhedra

The set of Archimedean Polyhedra contains five members formed by truncating the Platonic polyhedra.  These polyhedra contain truncated Petrie Polygons where edges of the Petrie Polygon of the Platonic polyhedron are alternated with added edges orthogonal to the symmetry axis of the Petrie Polygon.  

Petrie Expanded Truncated Platonic Polyhedra

Petrie Expanding the truncated Platonic Polyhedra results in a set of figures where the faces of the original Platonic polyhedron are separated by 'Petrie Hexagons' and the edges between an original Platonic face and a face generated by the original truncation are separated by squares.  The 'Petrie Hexagons' in each case have the same angles as those formed by the Petrie Expansion of the Platonic Polyhedra.


Petrie Expanded Truncated Tetrahedron (OFF)
(F,V,E)=(26,36,60) a=90°

Petrie Expanded Truncated Cube (OFF
(F,V,E)=(50,72,120) a=109.471°

Petrie Expanded Truncated Octahedron (OFF)
(F,V,E)=(50,72,120) a=70.529°

Petrie Expanded Truncated Dodecahedron (OFF)
(F,V,E)=(122,180,300) a=116.565°

Petrie Expanded Truncated Icosahedron (OFF)
(F,V,E)=(122,180,300) a=63.435°
 

Petrie Expanded Truncated Kepler-Poinsot Polyhedra


Petrie Expanded Great Truncated Dodecahedron (OFF)
(F,V,E)=(
122,180,300) a=63.435°

Petrie Expanded Great Truncated Icosahedron (OFF
(F,V,E)=(122,180,300) a=116.565°

Petrie Expanded Great Stellated Truncated Dodecahedron (OFF)
(F,V,E)=(114,180,300) a=138.19°

Petrie Expanded Small Stellated Truncated Dodecahedron (OFF)
(F,V,E)=(114,180,300) a=41.81°

Other Petrie Expanded Truncated Polyhedra


Petrie Expanded Stellated Truncated Hexahedron (OFF)
(F,V,E)=(
50,72,120) a=70.529°

Next: Skew Polygon Expanded Polyhedra

Index: Petrie Expanded Polyhedra