http://de.evo-art.org/index.php?action=history&feed=atom&title=Petrie_PolygonsPetrie Polygons - Versionsgeschichte2026-04-20T15:13:43ZVersionsgeschichte dieser Seite in de_evolutionary_art_orgMediaWiki 1.27.4http://de.evo-art.org/index.php?title=Petrie_Polygons&diff=4255&oldid=prevGbachelier: Die Seite wurde neu angelegt: „ == Reference == Paul Gailiunas: Petrie Polygons. In: Bridges 2003. Pages 503–510 == DOI == == Abstract == A Petrie polygon is a closed series of …“2015-01-31T21:12:33Z<p>Die Seite wurde neu angelegt: „ == Reference == Paul Gailiunas: <a href="/index.php?title=Petrie_Polygons" title="Petrie Polygons">Petrie Polygons</a>. In: <a href="/index.php?title=Bridges_2003" title="Bridges 2003">Bridges 2003</a>. Pages 503–510 == DOI == == Abstract == A Petrie polygon is a closed series of …“</p>
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== Reference ==<br />
Paul Gailiunas: [[Petrie Polygons]]. In: [[Bridges 2003]]. Pages 503–510 <br />
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== DOI ==<br />
<br />
== Abstract ==<br />
A Petrie polygon is a closed series of edges on a polyhedron (see Coxeter1 for a more detailed treatment). It is<br />
generally taken to mean an equatorial polygon (usually skew), for example the regular dodecahedron has six<br />
skew decagons with vertices that alternate across the equatorial planes parallel to its faces.<br />
<br />
A sequence of regular frameworks can be generated by moving the vertices of Petrie polygons anywhere<br />
between the equatorial planes and the ends of the axes perpendicular to the planes. The sequence passes<br />
through a position where the skew polygons define the edges of the original polyhedron, and the convex hull of<br />
the framework corresponds to the polyhedron .. The full sequence defines a series of polyhedra (which are<br />
isogonal if the original polyhedron is regular). Other isogonal polyhedra can be generated. (or example<br />
compounds of the antiprisms defined by each skew polygon.<br />
<br />
The vertices of moving frameworks generated from Platonic polyhedra define a conjugate framework which<br />
passes through an identical sequence. and also other frameworks that match the sequences generated by the<br />
dual Platonic polyhedron.<br />
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== Extended Abstract ==<br />
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== Bibtex == <br />
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== Used References ==<br />
Coxeter, H.S.M., Regular Polytopes, Third Edition, Dover Publications, 1973.<br />
<br />
Grünbaum, B., Polyhedra with Hollow Faces, Proc. NATO-ASI Conference on Polytopes: Abstract, Convex and Computational, Toronto, 1993.<br />
<br />
Cromwell, P.R., Polyhedra, CUP, 1997. (Plate 15)<br />
<br />
Fuller, R. Buckminster, Synergetics, Macmillan, 1982. (p. 212)<br />
<br />
Holden, A., Shapes, Space and Symmetry, Dover reprint,1991.<br />
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<br />
== Links ==<br />
=== Full Text === <br />
http://archive.bridgesmathart.org/2003/bridges2003-503.pdf<br />
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[[intern file]]<br />
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=== Sonstige Links ===<br />
http://archive.bridgesmathart.org/2003/bridges2003-503.html</div>Gbachelier