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The almost simple cubical polytopes

1998
*
Discrete Mathematics
*

We give a complete enumeration of all

doi:10.1016/s0012-365x(97)00159-3
fatcat:dluqv2lc6rhvtj3fj5xnbnkk5y
*the**almost**simple**cubical*d-*polytopes*for d/> 4, which is even valid for*almost**simple**cubical*(d-1)-spheres. ... A*cubical**polytope*is a convex*polytope*all of whose facets are combinatorial cubes. A d-*polytope*P is called*almost**simple*if, in*the*graph of P, each vertex of P is d-valent or (d + l )-valent. ... Clearly,*the*boundary complex of an*almost**simple**cubical*d-*polytope*is an*almost**simple**cubical*(d-1)-sphere. ...##
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Page 2359 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

In this paper,

*the*authors prove*the*following: If d > 4, then, with a single exception,*the**cubical*d-*polytopes*with at most 2/*! vertices are*almost**simple*. ... A convex d-*polytope*is*cubical*if all its facets are combinatorial (d — 1)-cubes, and is*almost**simple*if each of its vertices lies in d or d + | edges. ...##
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Page 4392 of Mathematical Reviews Vol. , Issue 98G
[page]

1998
*
Mathematical Reviews
*

Let P be a convex d-

*polytope*. P is called*cubical*if all its facets are combinatorial cubes. P is called*almost**simple*if each vertex of P is d-valent or (d + 1)-valent. ... Then P is*almost**simple*or a 2-fold 52 CONVEX AND DISCRETE GEOMETRY 4392 nonlinearly capped*polytope*. ...##
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Page 1839 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

We give a complete enumeration of all

*the**almost**simple**cubical*d-*polytopes*for d > 4, which is even valid for*almost**simple**cubical*(d — 1)-spheres. ... (D-STGT-B; Stuttgart)*The**almost**simple**cubical**polytopes*. (English summary) Discrete Math. 184 (1998), no. 1-3, 25-48. ...##
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Construction techniques for cubical complexes, odd cubical 4-polytopes, and prescribed dual manifolds
[article]

2004
*
arXiv
*
pre-print

We provide a number of new construction techniques for

arXiv:math/0310269v3
fatcat:dn2jsrowqzeejh6a7nrtfjqnnm
*cubical*complexes and*cubical**polytopes*, and thus for cubifications (hexahedral mesh generation). ... As an instance we obtain a*cubical*4-*polytope*with a cubation of Boy's surface as a dual manifold immersion, and with an odd number of facets. ...*The*illustrations of*polytopes*and balls were produced in*the*polymake system of Gawrilow & Joswig [14] , via javaview of Polthier et. al. [26] . (A small number of figures was drawn with xfig.) ...##
###
Construction Techniques for Cubical Complexes, Odd Cubical 4-Polytopes, and Prescribed Dual Manifolds

2004
*
Experimental Mathematics
*

*The*illustrations of

*polytopes*and balls were produced in

*the*polymake system of Gawrilow and Joswig [Gawrilow and Joswig 03], via javaview of Polthier et. al. [Polthier et al. 02]. ...

*The*second author was partially supported by

*the*Deutsche Forschungs-Gemeinschaft, via

*the*DFG Research Center "Mathematics in

*the*Key Technologies" (FZT86),

*the*Research Group "Algorithms, Structure, ...

*Almost*

*Cubical*

*Polytopes*All proper faces of a

*cubical*d-

*polytope*have to be combinatorial cubes. ...

##
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Torus actions, combinatorial topology and homological algebra
[article]

2000
*
arXiv
*
pre-print

*The*paper surveys some new results and open problems connected with such fundamental combinatorial concepts as

*polytopes*, simplicial complexes,

*cubical*complexes, and subspace arrangements. ... Particular attention is paid to

*the*case of simplicial and

*cubical*subdivisions of manifolds and, especially, spheres. ... Each face of a

*simple*

*polytope*is a

*simple*

*polytope*.

*The*product P 1 × P 2 of two

*simple*

*polytopes*P 1 and P 2 is a

*simple*

*polytope*as well. ...

##
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Isocanted alcoved polytopes
[article]

2020
*
arXiv
*
pre-print

Isocanted alcoved

arXiv:2009.13858v1
fatcat:v764dqzwrre5fjhk2npaumoe4a
*polytopes*are centrally symmetric,*almost**simple**cubical**polytopes*. They are zonotopes. We show that, for each dimension, there is a unique combinatorial type. ... They are realizations of d–elementary*cubical**polytopes*.*The*f–vector of a d–dimensional isocanted alcoved*polytope*attains its maximum at*the*integer ⌊ d/3⌋. ... Further properties are proved, showing that isocanted alcoved*polytopes*are d-elementary*cubical*,*almost**simple*and zonotopes. ...##
###
Combinatorial Space Tiling
[article]

2010
*
arXiv
*
pre-print

*The*present article studies combinatorial tilings of Euclidean or spherical spaces by

*polytopes*, serving two main purposes: first, to survey some of

*the*main developments in combinatorial space tiling; ...

*The*tiling properties of

*simple*convex

*polytopes*are not well understood. Recall here that a convex d-

*polytope*is called

*simple*if all its vertices are d-valent. ... It may be conjectured that every

*simple*convex 3-

*polytope*is

*the*prototile of a monotypic face-to-face tiling of E 3 by topological

*polytopes*. ...

##
###
Site percolation and random walks ond-dimensional Kagomé lattices

1998
*
Journal of Physics A: Mathematical and General
*

These lattices are isotropic and have

doi:10.1088/0305-4470/31/15/010
fatcat:pvidzbo2mbhexedmuqq3tieayu
*the*same coordination number q as*the*hyper-*cubic*lattices in d dimensions, namely q=2d. ...*The*site percolation problem is studied on d-dimensional generalisations of*the*Kagome' lattice. ... Acknowledgments I would like to thank Ed Stephens for critically reading*the*manuscript and Shell International Exploration & Production for permission to publish this paper. ...##
###
Page 6816 of Mathematical Reviews Vol. , Issue 2000j
[page]

2000
*
Mathematical Reviews
*

a nonabelian

*simple*group such that L < G < Aut(L)—from*the*fact that G is an*almost**simple*group—an2¢d it is identical with*the*socle of G). ... It is also proved that AutI’ is an*almost**simple*group. ...##
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Normal crossing immersions, cobordisms and flips
[article]

2020
*
arXiv
*
pre-print

We study various analogues of theorems from PL topology for

arXiv:2001.01108v1
fatcat:mchimpjprrgrlm6bivawczxjxm
*cubical*complexes. ... In particular, we characterize when two PL homeomorphic cubulations are equivalent by Pachner moves by showing*the*question to be equivalent to*the*existence of cobordisms between generic immersions of ... In*cubical*complexes, popularized for their connection to low-dimensional topology and geometric group theory,*the*situation is not as*simple*. ...##
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POLYTOPES AND PROJECTION METHOD : AN APPROACH TO COMPLEX STRUCTURES

1986
*
Le Journal de Physique Colloques
*

Abstract: Decoration with atomic motifs in high dimension space is considered in

doi:10.1051/jphyscol:1986330
fatcat:3wnukkfcz5apxluqxoqulswccm
*simple*cases, and related to*the*theory of curved spaces in non-periodic structures. ... Great -Britain ~ksurn6: La mise en place de motifs atomlques dans les espaces de grandes dimensions est envisagde dans des cas*simples*en rapport avec la thgorie des espaces courbes pour les structures ...*The**simple*plane surface in a*cubic*lattice (1,0,0) leads to twinning defects. (Fig. 9 ). 2. ...##
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Page 4194 of Mathematical Reviews Vol. , Issue 2000f
[page]

2000
*
Mathematical Reviews
*

(CZ-KARL-AM; Prague)

*Almost*-tiling*the*plane by ellipses. (English summary) Discrete Comput. Geom. 22 (1999), no. 3, 367-375. ... Summary: “*The*universal*polytope*is*the**polytope*defined as*the*convex hull of*the*characteristic vectors of all triangulations for a given point configuration. ...##
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Non-constructible Complexes and the Bridge Index

2001
*
European journal of combinatorics (Print)
*

We show that if a three-dimensional

doi:10.1006/eujc.2000.0477
fatcat:xlui4nc6ang7vjm5x3uvndpnua
*polytopal*complex has a knot in its 1-skeleton, where*the*bridge index of*the*knot is larger than*the*number of edges of*the*knot, then*the*complex is not constructible ... As an application we settle a conjecture of Hetyei concerning*the*shellability of*cubical*barycentric subdivisions of 3-spheres. ...*The*second author was supported by Research Fellowships of*the*Japan Society for*the*Promotion of Science for Young Scientists. ...
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