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...[[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 ...

| Type=[[Regular projective 4-polytope]] ...r1-link = Peter McMullen | first2 = Egon | last2 = Schulte | chapter = 6C. Projective Regular Polytopes | title = Abstract Regular Polytopes | edition = 1st | pu ...

...er]] looked at skew vertex figures which created new 4-dimensional regular polyhedra, and much later [[Branko Grünbaum]] looked at regular skew faces.<ref>Abstr Infinite regular skew polyhedra that span 3-space or higher are called [[regular skew apeirohedron|regular ...

...a two-dimensional [[manifold]] (such as a [[sphere]], [[torus]], or [[real projective plane]]) into topological disks such that every [[Flag (geometry)|flag]] (a ...e [[Hemicube (geometry)|hemicube]] is a regular map of type {4,3} in the [[projective plane]]. ...

...of two- and three-dimensional integral polytopes may be called polygons or polyhedra instead of polytopes, respectively. Some polyhedra arising from [[combinatorial optimization]] problems are automatically inte ...

...gth less than one,<ref>{{KlitzingPolytopes|polyhedra.htm|3D convex uniform polyhedra|x3o4o - oct}} 1/sqrt(2) = 0.707107</ref> the triangular pyramids can be mad ...jecture]], that the connected graphs with [[planar cover]]s are themselves projective-planar.<ref>{{citation ...

...omorphisms between the series of [[finite simple group]]s mostly involve [[projective special linear group]]s and [[alternating group]]s, and are:{{sfn|ps=|Wilso ...≅ PSp{{sub|4}}(3), between a [[projective special unitary group]] and a [[projective symplectic group]]. ...

...theorems about the structure of the set of Chern numbers of smooth complex-projective manifolds. ...anched covering''. Kotschick's analysis also applies to [[fullerene]]s and polyhedra that Kotschick calls ''generalized soccer balls''.<ref name=AmSci/><ref>{{c ...

...h degrees of the fundamental invariants 3, 6, and 12, which can be seen in projective symmetry of the polytopes. == Related complex polyhedra== ...

...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 ...

| title = Polyhedra: One of the most charming chapters of geometry ...ed a 75-year-old omission in [[Evgraf Fedorov]]'s classification of convex polyhedra with congruent [[Rhombus|rhombic]] faces.<ref name="grun"/> ...

...xplored by [[Leonhard Euler|Euler]], who conjectured that all [[Polyhedron|polyhedra]] in <math>3</math>-dimensions are rigid. Much work has gone into proving === Polyhedra === ...

...re 40 [[hyperplane]]s contain central [[Hessian polyhedron#Related complex polyhedra|₃{3}₃{4}₂]], {{CDD|3node_1|3|3node|4|node} ...being a ''Witting [[Configuration (polytope)|configuration]]'' in complex projective 3-space:<ref>Alexander Witting, Ueber Jacobi'sche Functionen k<sup>ter</sup ...

..., and in three-dimensional space it is a [[twisted cubic]]. Its closure in projective space is the [[rational normal curve]]. ...ion = Complexity of Delaunay triangulation for points on lower-dimensional polyhedra ...

...1}; geometrically, quotienting out by this corresponds to passing to the [[projective orthogonal group]]. ...he subquotient (derived subgroup, mod center) is the symmetry group of the projective demihypercube. ...

...spaces are constructed using projective equivalence of schemes in a fixed projective space on a fixed [[Hilbert scheme]]</ref> Now, using [[Serre duality]] and ...h>X_\psi</math> called the [[Dwork family]]. It is the [[Proj construction|projective family]] ...

...ce]]<ref>{{Cite journal |last1=Zariski, O. |title=On the Poincaré group of projective hypersurface |date=1937 |volume=38 |issue=1 |journal=Ann. of Math. |pages=1 ...neighboring points.<ref>{{Cite journal |last1=Varchenko, A. |title=Newton Polyhedra and Asymptotics of Oscillatory Integrals |date=1976 |volume=10 |issue=3 |jo ...

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

* smooth compact polyhedra in a smooth manifold <math>X</math> ...<math>\mathcal P(X)</math> denote the collection of compact differentiable polyhedra in <math>X.</math> The normal cycle <math>N(A)\subset \mathbb P_X</math> o ...

..., Huyk Kim and Hyunkoo Lee proved for affine manifolds, and more generally projective manifolds developing into an affine space with amenable [[holonomy]] by a d * E. Bloch, The angle defect for arbitrary polyhedra, Beiträge zur Algebra und Geometrie, volume 39 (1998), pp.379–393 ...