Quelltext der Seite Petrie Polygons


== Reference ==
Paul Gailiunas: [[Petrie Polygons]]. In: [[Bridges 2003]]. Pages 503–510 

== DOI ==

== Abstract ==
A Petrie polygon is a closed series of edges on a polyhedron (see Coxeter1 for a more detailed treatment). It is
generally taken to mean an equatorial polygon (usually skew), for example the regular dodecahedron has six
skew decagons with vertices that alternate across the equatorial planes parallel to its faces.

A sequence of regular frameworks can be generated by moving the vertices of Petrie polygons anywhere
between the equatorial planes and the ends of the axes perpendicular to the planes. The sequence passes
through a position where the skew polygons define the edges of the original polyhedron, and the convex hull of
the framework corresponds to the polyhedron .. The full sequence defines a series of polyhedra (which are
isogonal if the original polyhedron is regular). Other isogonal polyhedra can be generated. (or example
compounds of the antiprisms defined by each skew polygon.

The vertices of moving frameworks generated from Platonic polyhedra define a conjugate framework which
passes through an identical sequence. and also other frameworks that match the sequences generated by the
dual Platonic polyhedron.

== Extended Abstract ==

== Bibtex == 

== Used References ==
Coxeter, H.S.M., Regular Polytopes, Third Edition, Dover Publications, 1973.

Grünbaum, B., Polyhedra with Hollow Faces, Proc. NATO-ASI Conference on Polytopes: Abstract, Convex and Computational, Toronto, 1993.

Cromwell, P.R., Polyhedra, CUP, 1997. (Plate 15)

Fuller, R. Buckminster, Synergetics, Macmillan, 1982. (p. 212)

Holden, A., Shapes, Space and Symmetry, Dover reprint,1991.


== Links ==
=== Full Text === 
http://archive.bridgesmathart.org/2003/bridges2003-503.pdf

[[intern file]]

=== Sonstige Links ===
http://archive.bridgesmathart.org/2003/bridges2003-503.html