This is an indexed list of the uniform and stellated polyhedra from the book ''Polyhedron Models'', by

Magnus Wenninger Father Magnus J. Wenninger OSB (October 31, 1919Banchoff (2002)– February 17, 2017) was an American mathematician who worked on constructing polyhedron models, and wrote the first book on their construction. Early life and education Born to ...

. 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 In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows that all vertices are congruent. Uniform polyhedra may be regular (if also fac ...

, as well as 44 stellated forms of the convex regular and quasiregular polyhedra. Models listed here can be cited as "Wenninger Model Number ''N''", or ''W''_''N'' for brevity. The polyhedra are grouped 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 In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edge ...
(regular convex polyhedra) W1 to W5

Archimedean solids The Archimedean solids are a set of thirteen convex polyhedra whose faces are regular polygon and are vertex-transitive, although they aren't face-transitive. The solids were named after Archimedes, although he did not claim credit for them. They ...
(Semiregular) W6 to W18

Kepler–Poinsot polyhedra (Regular star polyhedra) W20, W21, W22 and W41

Stellations: models W19 to W66

Stellations of octahedron

Stellations of dodecahedron

Stellations of icosahedron

Stellations of cuboctahedron

Stellations of icosidodecahedron

Uniform nonconvex solids W67 to W119

References

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

External links

Magnus J. Wenninger
* Software used to generate images in this article: *
Stella: Polyhedron Navigator

Stella (software) Stella is a computer program available in three versions (Great Stella, Small Stella and Stella4D). It was created by Robert Webb of Australia. The programs contain a large library of polyhedra which can be manipulated and altered in various w ...

- Can create and print nets for all of Wenninger's polyhedron models. *
Vladimir Bulatov's Polyhedra Stellations Applet
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Vladimir Bulatov's Polyhedra Stellations Applet packaged as an OS X application

known errors in the various editions. {{DEFAULTSORT:Wenninger Polyhedron Models Polyhedra Polyhedral stellation Mathematics-related lists

Platonic solids In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edge ... (regular convex polyhedra) W1 to W5

Archimedean solids The Archimedean solids are a set of thirteen convex polyhedra whose faces are regular polygon and are vertex-transitive, although they aren't face-transitive. The solids were named after Archimedes, although he did not claim credit for them. They ... (Semiregular) W6 to W18