Petrie schemes
G Williams - Canadian Journal of Mathematics, 2005 - cambridge.org
… complexes. A Petrie polygon of a polyhedron is a sequence of edges of the polyhedron
where any two consecutive elements of the sequence have a vertex and face in common,
but no three consecutive edges share a common face …
where any two consecutive elements of the sequence have a vertex and face in common,
but no three consecutive edges share a common face …
On the number of sides of a Petrie polygon
R Steinberg - Canadian Journal of Mathematics, 1958 - cambridge.org
Let {p, q, r} be the regular 4-dimensional poly tope for which each face is a {p, q} and each
vertex figure is a {q, r}, where {p, q}, for example, is the regular polyhedron with p-gonal
faces, q at each vertex. A Petrie polygon of {p, q} is a skew polygon made up of edges of {p …
vertex figure is a {q, r}, where {p, q}, for example, is the regular polyhedron with p-gonal
faces, q at each vertex. A Petrie polygon of {p, q} is a skew polygon made up of edges of {p …
A new Petrie-like construction for abstract polytopes
MI Hartley, D Leemans - Journal of Combinatorial Theory, Series A, 2008 - Elsevier
… Keywords: Abstract regular polytopes; Petrial 1. Introduction The history of the study of regular
polyhedra and regular polytopes began an important turning point when Coxeter popularised,
in Section 2 of [1], the concept of the “Petrie polygon” of a polyhedron …
polyhedra and regular polytopes began an important turning point when Coxeter popularised,
in Section 2 of [1], the concept of the “Petrie polygon” of a polyhedron …
Cell decompositions of the projective plane with Petrie polygons of constant length
J Bokowski, JP Roudneff, TK Strempel - Discrete & Computational …, 1997 - Springer
… induced cell de- compositions (DS2 , D∗ S2 ) on the 2-sphere S2 form dual pairs of combinatorical
types of convex polyhedra, and such that these dual pairs share two natural properties with those
induced by dual pairs of Platonic solids: (1) Every Petrie polygon is a finite …
types of convex polyhedra, and such that these dual pairs share two natural properties with those
induced by dual pairs of Platonic solids: (1) Every Petrie polygon is a finite …
Petrie polygons, Fibonacci sequences and Farey maps
D Singerman, J Strudwick - Ars Mathematica Contemporanea, 2016 - amc-journal.eu
… Keywords: Regular map, Petrie polygon, Fibonacci sequence. Math. Subj. Class.: 05C10, 11B39,
20H05 1 Introduction … A Petrie polygon on a regular map is a zig-zag path through the map and
an important invariant of a regular map is the length of a Petrie polygon …
20H05 1 Introduction … A Petrie polygon on a regular map is a zig-zag path through the map and
an important invariant of a regular map is the length of a Petrie polygon …
[CITATION][C] Ten toroids and fifty-seven hemi-dodecahedra
HSM Coxeter - Geometriae dedicata, 1982 - Springer
… 2. TWISTED HONEYCOMBS \ For a regular polyhedron or tessellation or map {p, q} (with p-gonal
faces, q round each vertex), a Petrie polygon is a skew polygon such that every two consecutive
edges (or sides), but no three, belong to a face [Coxeter, 1939, p. 128] …
faces, q round each vertex), a Petrie polygon is a skew polygon such that every two consecutive
edges (or sides), but no three, belong to a face [Coxeter, 1939, p. 128] …
[CITATION][C] Close-packing and froth
HSM Coxeter - Illinois Journal of Mathematics, 1958 - projecteuclid.org
… consecutive integers. A Petrie polygon of {p, q} is a skew 2c-gon whose sides are 2c
edges of the solid, so chosen that any two consecutive sides, but no three, belong to
a face; eg, the Petrie polygon of a cube isa skew hexagon. Every …
edges of the solid, so chosen that any two consecutive sides, but no three, belong to
a face; eg, the Petrie polygon of a cube isa skew hexagon. Every …
My graph
HSM Coxeter - Proceedings of the London Mathematical …, 1983 - academic.oup.com
… 1 as a perspective view of the regular dodecahedron {5, 3} (pentagonal faces, three at each vertex),
the peripheral decagon represents a skew decagon of the kind that is called a Petrie polygon:
every two adjacent edges belong to one face, but the next edge of the skew …
the peripheral decagon represents a skew decagon of the kind that is called a Petrie polygon:
every two adjacent edges belong to one face, but the next edge of the skew …
[PDF][PDF] Pseudo-Petrie operators on Grünbaum polyhedra
C Leytem - Mathematica Slovaca, 1997 - dml.cz
… We are going to prove it is the 48th Grunbaum polyhedron {cot'- ?,4}, To this effect we need a
few lemmas. LEMMA 3.2.1. a) There exists a screw transformation s of a polyhedron P which
trans- forms a pseudo-Petrie polygon denoted [... W1? W2, W3, W4, W5, W6 …
few lemmas. LEMMA 3.2.1. a) There exists a screw transformation s of a polyhedron P which
trans- forms a pseudo-Petrie polygon denoted [... W1? W2, W3, W4, W5, W6 …
A census of regular 3-polystroma arising from honeycombs
CJ Colbourn, AI Weiss - Discrete mathematics, 1984 - Elsevier
… 2. Regular raps A regular tessellation or map {p, q} is a collection of p-gonal faces,
q meeting at each vertex. The Petrie polygon of such a map is a skew polygon in which
every two, but not three, consecutive edges belong to a face …
q meeting at each vertex. The Petrie polygon of such a map is a skew polygon in which
every two, but not three, consecutive edges belong to a face …