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|bgcolor=#e7dcc3|Properties||convex, chiral == Related polyhedra== ...

|+ Icosahedral Goldberg polyhedra, {{nobr|with pentagons in red}} Simple examples of Goldberg polyhedra include the [[dodecahedron]] and [[truncated icosahedron]]. Other forms can ...

| footer = An [[icosahedron]] and related symmetry polyhedra can be used to define a high geodesic polyhedron by dividing triangular [[F ...les can then be further subdivided into smaller triangles for new geodesic polyhedra. All vertices are valence-6 except the 12 centered at the original vertices ...

...hich is regular but not reflexible is said to be [[Chirality (mathematics)|chiral]]. ==Toroidal polyhedra== ...

...s required to form a icositetahedron.<ref>{{Cite web |title=Enumeration of Polyhedra - Numericana |url=http://www.numericana.com/data/polycount.htm |access-date There are many symmetric forms, and the ones with highest symmetry have chiral [[icosahedral symmetry]]: ...

...ree intertwined [[helix|helices]]. There are two [[Chirality (mathematics)|chiral]] forms, with either clockwise or counterclockwise windings. Unlike any oth ...integer. The two different values of <math>\theta</math> correspond to two chiral forms. All vertices are located on the cylinder with radius <math> r </math ...

...[geometry]]. He has made major contributions in the study of regular and [[chiral polytope]]s whose [[automorphism group]]s are finite almost simple groups. | title=Chiral polyhedra and finite simple groups ...

...und of five tetrahedra]] expresses the exceptional isomorphism between the chiral icosahedral group and the alternating group on five letters.]] ...[[regular polyhedra]]: the alternating group A₅ agrees with the chiral [[icosahedral group]] (itself an exceptional object), and the [[covering gr ...

...n (3,1) and geodesic polyhedron (3,1). The Goldberg polyhedra and geodesic polyhedra were precursors to the Goldberg–Coxeter operation. ...T|doi-access=free }}</ref> and the general study of [[graph theory]] and [[polyhedra]].<ref>{{cite journal|doi=10.1016/j.ejc.2017.08.004|title=Packing and cover ...

...ssen]], who studied it in 1967.{{r|jessen}} In 1971, a family of nonconvex polyhedra including this shape was independently discovered and studied by [[Adrien D ...sis for the construction of an infinite family of combinatorially distinct polyhedra with right dihedral angles, formed by gluing copies of Jessen's icosahedron ...

...001, she graduated in [[Mathematics]] with a baccalaureate thesis titled ''Polyhedra colored with cyclic orders''.<ref name="vuelven">{{Cite web|url=http://www. | title=Construction of chiral 4-polytopes with alternating or symmetric automorphism group ...

...dissected into some integral number of it. The characteristic simplex is [[chiral]] (it comes in two mirror-image forms which are different), and the polytop | title = Volumes of non-Euclidean polyhedra ...

...e regions of space nearest each vertex of the graph are congruent 17-sided polyhedra that tile space. Its edges lie on diagonals of the [[regular skew polyhedro ...n be realized by a symmetry. However, the overall structure is [[Chirality|chiral]]: no sequence of translations and rotations can make it coincide with its ...

The '''chiral hyper-octahedral symmetry''', is the direct subgroup, index 2 of hyper-octa ...''', by dimension:<ref>{{harvnb|Coxeter|1999|p=121, Essay 5 ''Regular skew polyhedra''}}</ref> These groups have ''n'' orthogonal mirrors in ''n''-dimensions. ...

{{short description|Tiling of hyperbolic 3-space by uniform polyhedra}} ...dron|icosidodecahedra]], and cubes. (The version with tetrahedral-symmetry polyhedra is the cubic-octahedral honeycomb, using cuboctahedra, octahedra, and cubes ...

...cing pyritohedral generators {0,12}, a reflection and 3-fold rotation. And chiral tetrahedral symmetry can be written as {{CDD|node_h0|4|node_h2|3|node_h2}} ...polyhedra [[icosahedron]] becomes [5/2,5], the symmetry of 2 regular star polyhedra. It also relates the hyperbolic tilings {p,3}, and [[List of regular polyto ...

!Chiral<br>extended<br>symmetry !Chiral<br>extended<br>symmetry ...