List of Wenninger polyhedron models


List of Wenninger polyhedron models

This table contains an indexed list of the Uniform and stellated polyhedra from the book "Polyhedron Models", by Magnus Wenninger.

The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes.

It contains the 75 nonprismatic uniform polyhedra, as well as 44 stellated forms of the convex regular polyhedra.

This list was written to honor this early polyhedral work from Wenninger, and to provide a detailed reference to the 119 numbered models in his book.

Models listed here can be cited as "Wenninger Model Number N", or WN for brevity.

The polyhedra are grouped below in 5 tables: Regular (1-5), Semiregular (6-18), regular star polyhedra (20-22,41), Stellations and compounds (19-66), and uniform star polyhedra (67-119). "The four regular star polyhedra are listed twice because they belong to both the uniform polyhedra and stellation groupings."

Platonic solids (Regular) W1 to W5

tellations: models W19 to W66

tellations of octahedron

tellations of cuboctahedron

References

*
** Errata
*** In Wenninger, the vertex figure for W90 is incorrectly shown as having parallel edges.
*

External links

* [http://employees.csbsju.edu/mwenninger Magnus J. Wenninger]
* Software used to generate images in this article:
** [http://www.software3d.com/Stella.php Stella: Polyhedron Navigator] Stella (software) - Can create and print nets for all of Wenninger's polyhedron models.
** [http://bulatov.org/old/polyhedra/stellation_applet Vladimir Bulatov's Polyhedra Stellations Applet]
* [http://www.software3d.com/UsersModels.php Gallery of Polyhedron Models]
* [http://www.steelpillow.com/polyhedra/Wenninger/Wenninger.html M. Wenninger, "Polyhedron Models", Errata] : known errors in the various editions.
* [http://www.lifeisastoryproblem.org/explore/net_stellated_dodecahedron.pdf Printable Net of a Stellated Dodecahedron] [http://www.lifeisastoryproblem.org Life is a Story Problem.org]


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Polyhedron — Polyhedra redirects here. For the relational database system, see Polyhedra DBMS. For the game magazine, see Polyhedron (magazine). For the scientific journal, see Polyhedron (journal). Some Polyhedra Dodecahedron (Regular polyhedron) …   Wikipedia

  • List of mathematics articles (L) — NOTOC L L (complexity) L BFGS L² cohomology L function L game L notation L system L theory L Analyse des Infiniment Petits pour l Intelligence des Lignes Courbes L Hôpital s rule L(R) La Géométrie Labeled graph Labelled enumeration theorem Lack… …   Wikipedia

  • List of uniform polyhedra — Uniform polyhedra and tilings form a well studied group. They are listed here for quick comparison of their properties and varied naming schemes and symbols.This list includes: * all 75 nonprismatic uniform polyhedra; * a few representatives of… …   Wikipedia

  • List of uniform polyhedra by vertex figure — There are many relations among the uniform polyhedron.Some are obtained by truncating the vertices of the regular or quasi regular polyhedron.Others share the same vertices and edges as other polyhedron.The grouping below exhibit some of these… …   Wikipedia

  • Magnus Wenninger — in 2009 in his office with many of his models and a visiting theology student Father Magnus J. Wenninger OSB (born Park Falls, Wisconsin, October 31, 1919) is a mathematician who works on constructing polyhedron models, and wrote the first book… …   Wikipedia

  • Uniform polyhedron — A uniform polyhedron is a polyhedron which has regular polygons as faces and is transitive on its vertices (i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high… …   Wikipedia

  • Kepler–Poinsot polyhedron — In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. They may be obtained by stellating the regular convex dodecahedron and icosahedron, and differ from these in having regular pentagrammic faces or vertex figures.… …   Wikipedia

  • Omnitruncated polyhedron — In geometry, an omnitruncated polyhedron is a truncated quasiregular polyhedron. When they are alternated, they produce the snub polyhedra. All omnitruncated polyhedra are zonohedra. They have Wythoff symbol p q r | and vertex figures as 2p.2q.2r …   Wikipedia

  • Uniform star polyhedron — A display of uniform polyhedra at the Science Museum in London …   Wikipedia

  • Stellation — is a process of constructing new polygons (in two dimensions), new polyhedra in three dimensions, or, in general, new polytopes in n dimensions. The process consists of extending elements such as edges or face planes, usually in a symmetrical way …   Wikipedia


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.