Pseudo-Petrie operators on Grünbaum polyhedra. (English) Zbl 1023.52002

Summary: It is introduced and studied the pseudo-Petrie operator, its properties, and the semi-regular polyhedra it produces. As a consequence, we obtain the 48th Grünbaum polyhedron as the pseudo-Petrie polyhedron of one of the 47 Grünbaum polyhedra.


52B10 Three-dimensional polytopes
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[1] COXETER H. S. M.: Regular Polytopes. Dover Publications, New York, 1973. · Zbl 0031.06502
[2] DRESS A.: A combinatorial theory of Gruenbaum’s new regular polyhedra. Aequationes Math. 29 (1985), 222-243. · Zbl 0588.51022 · doi:10.1007/BF02189831
[3] GRUNBAUM B.: Regular polyhedra - old and new. Aequationes Math. 16 (1977), 1-20.
[4] McMULLEN P.-SCHULTE E.: Constructions for regular polytopes. J. Combin. Theory Ser. A 53 (1990), 1-28. · Zbl 0689.51009 · doi:10.1016/0097-3165(90)90017-Q
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