Search results

| contribution = IX.4: Polyhedra with ring-shaped faces == In polyhedra== ...

...triacontahedron and the 30 rhombic prisms are removed, you can create a [[toroidal polyhedron]] with all regular polygon faces. == Related polyhedra == ...

...e, and 24 [[triangular prism]]s. <ref>{{Cite web|url=http://www.doskey.com/polyhedra/PrismExpansions.html|title = Prism Expansions}}</ref> It has 148 faces (8 t Without the triangular prisms, the toroidal polyhedron becomes a truncated cuboctahedron. ...

...dimensional features, and counting how many facets it passes through. For polyhedra for which this count does not depend on the choice of the ray, and for whic ...by choosing any point interior to the polyhedron as its center. For these polyhedra, the density will be&nbsp;1. ...

==Toroidal polyhedra== Regular maps exist as torohedral polyhedra as finite portions of Euclidean tilings, wrapped onto the surface of a [[du ...

...lyhedron]] with all regular polygon faces.<ref>[http://www.orchidpalms.com/polyhedra/rhombic/RD/XRD-dissection.htm A Dissection of the Expanded Rhombic Dodecahe == Related polyhedra== ...

...an form the faces of [[Simple polytope|simple]] [[convex polyhedron|convex polyhedra]]. It states that, for given numbers of triangles, quadrilaterals, pentagon ...888 in his [[habilitation]] thesis and in expanded form in an 1891 book on polyhedra.{{r|cp|zmp|ve}} ...

...[[spherical polyhedra]] – tessellations of the [[sphere]] – and [[toroidal polyhedra]] – tessellations of the toroids. Projective polyhedra are also referred to as '''elliptic tessellations'''<ref>{{Cite book ...

==Regular polyhedra== ...of the [[hexagonal tiling]] as type [[Regular map (graph theory)#Toroidal polyhedra|{6,3}_(2,0)]]. ...

Several distinguished [[polyhedra]] in [[Three-dimensional space|three dimensions]] contain fourteen [[Face ( ...l-access=registration |title=Regular Polytopes |chapter=Chapter 2: Regular polyhedra |publisher=Dover |edition=3rd |location=New York |year=1973 |pages=18–19 |i ...

...on-adjacent pair of vertices is the diagonal of a unique square. It is a [[toroidal graph]], a [[locally linear graph]], a [[strongly regular graph]] with para ...over Publications, 1999, {{ISBN|0-486-40919-8}} (Chapter 5: Regular Skew Polyhedra in three and four dimensions and their topological analogues) ...

* [[Toroidal polyhedron]] ...University of California Press |isbn=978-0-520-03056-5 |chapter=5. Joining polyhedra §5.36 Tetrahelix |page=53}} ...

...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 ...

The value of the [[Euler characteristic]] used to characterise polyhedra does not generalize usefully to higher dimensions, and is zero for all 10-p ...y of a polyhedron is insufficient to characterise the surface twistings of toroidal polytopes, and this led to the use of torsion coefficients.<ref name="riche ...

...tex, edge, and face) into any other flag.<ref>{{citation|title=The regular polyhedra of type {''p'', 3} with 2''p'' vertices|first=Peter|last=McMullen|authorlin One of these two embeddings forms a [[torus]], so the Nauru graph is a [[toroidal graph]]: it consists of 12 hexagonal faces together with the 24 vertices an ...

{{Short description|Graph-theoretic description of polyhedra}} {{about|the theorem on graphs of polyhedra}} ...

Analogous results for [[Toroidal graph|graphs embedded on a torus]] were independently proved ...will find an embedding that realizes all facets of the polytope as convex polyhedra.<ref>{{citation ...