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...link=Igor Shafarevich |first=I.R. |last=Shafarevich |title=Basic Algebraic Geometry |url=https://books.google.com/books?id=m6nwCAAAQBAJ |date=2012 |publisher=S Multi-homogeneous Bézout theorem provides such a better bound when the unknowns m ...

...out any notion of distance. Seven-dimensional [[Euclidean space]] is seven-dimensional space equipped with a [[Euclidean metric]], which is defined by the [[dot p ...] vector space, which has 14 real dimensions. It may also refer to a seven-dimensional [[manifold]] such as a [[7-sphere]], or a variety of other geometric constr ...

...e spheres, cylinders, and cones, which can be infinite or finite. Some two-dimensional mathematical spaces are not used to represent physical positions, like an [ ...f them are [[parallel lines|parallel]], meaning they never [[intersection (geometry)|intersect]] and stay at uniform distance from each-other. ...

...ied 5-cube''' is a convex [[uniform 5-polytope]], being a [[Rectification (geometry)|rectification]] of the regular [[5-cube]]. ...ectified 5-cube may be constructed from the [[5-cube]] by [[Rectification (geometry)|truncating]] its vertices at the midpoints of its edges. ...

...ter group]]. The family was named by [[H. S. M. Coxeter]], because the two-dimensional pentagonal polytope is a [[pentagon]]. It can be named by its [[Schläfli sy ...ytope|1-polytopes]] and ends with ''n'' = 5 as infinite tessellations of 4-dimensional hyperbolic space. ...

In geometry, it is an unsolved [[conjecture]] of [[Hugo Hadwiger]] that every [[simplex ...ce). The points that form the simplex in this way are called its [[vertex (geometry)|vertices]]. ...

...out any notion of distance. Eight-dimensional [[Euclidean space]] is eight-dimensional space equipped with the [[Euclidean metric]]. ...vector space, which has 16 real dimensions. It may also refer to an eight-dimensional [[manifold]] such as an [[8-sphere]], or a variety of other geometric const ...

In [[geometry]] of 4 dimensions or higher, a '''proprism''' is a [[polytope]] resulting f The number of [[Vertex (geometry)|vertices]] in a proprism is equal to the product of the number of vertices ...

...vtxt|Błocki|2014a}} and {{harvtxt|Błocki|Zwonek|2020}}. The multi (high) - dimensional Suita conjecture fails in non-[[pseudoconvex domain]]s.<ref>{{harvtxt|Nikol ...=Suita Conjecture from the One-dimensional Viewpoint |title=Analysis Meets Geometry |series=Trends in Mathematics |year=2017 |last1=Błocki |first1=Zbigniew |pa ...

...6-simplex''' is a convex [[uniform 6-polytope]], being a [[Rectification (geometry)|rectification]] of the regular [[6-simplex]]. ...as permutations of (0,0,0,0,0,1,1). This construction is based on [[Facet (geometry)|facets]] of the [[rectified 7-orthoplex]]. ...

...ied 6-cube''' is a convex [[uniform 6-polytope]], being a [[Rectification (geometry)|rectification]] of the regular [[6-cube]]. ...ectified 6-cube may be constructed from the [[6-cube]] by [[Rectification (geometry)|truncating]] its vertices at the midpoints of its edges. ...

...a function of spatial frequency.{{sfn|ps=|Unser|Trus|Steven|1987}} It is a multi-particle extension of the [[Fourier ring correlation]] (FRC), which is rela | title = Exact filters for general geometry three dimensional reconstruction ...

...-orthoplex''' is a convex [[uniform 5-polytope]], being a [[Rectification (geometry)|rectification]] of the regular [[5-orthoplex]]. ...entifying it as Cr₅¹ as a first rectification of a 5-dimensional [[cross polytope]]. ...

...9|issue=3|year=1975|pages= 1–4|mr=0435072}}</ref> and {{Interlanguage link multi|Anatoliy Kushnirenko|ru|3=Кушниренко, Анатолий Георгиевич}}<ref>{{citation| where each <math>f_i</math> is a generic element in the (finite dimensional vector space) <math>L_{A_i}.</math> ...

...ional [[String (physics)|string]], or a two-dimensional membrane to higher-dimensional objects. Branes are [[dynamical system| dynamical]] objects which can propa ...cs]] for insight into [[homological mirror symmetry]] and [[noncommutative geometry]]. ...

...ted hexeract''') is a convex [[uniform 6-polytope]], being a [[Truncation (geometry)|truncation]] of the regular [[6-cube]]. The truncated 6-cube may be constructed by [[Truncation (geometry)|truncating]] the vertices of the [[6-cube]] at <math>1/(\sqrt{2}+2)</math> ...

...ms/cag/content/vols/0020/0003/a004/|journal=Communications in Analysis and Geometry|volume=20|issue=3|pages=529–563|doi=10.4310/CAG.2012.v20.n3.a4|arxiv=0908.1 ...exists a more succinct geometric definition using the language of [[formal geometry]]. Here the blanket assumption that the underlying field is of characterist ...

In six-dimensional [[geometry]], a '''cantellated 6-simplex''' is a convex [[uniform 6-polytope]], being ...as permutations of (0,0,0,0,1,1,2). This construction is based on [[Facet (geometry)|facets]] of the [[cantellated 7-orthoplex]]. ...

...ncated 5-cube''' is a convex [[uniform 5-polytope]], being a [[Truncation (geometry)|truncation]] of the regular [[5-cube]]. The ''truncated 5-cube'' may be constructed by [[Truncation (geometry)|truncating]] the vertices of the [[5-cube]] at <math>1/(\sqrt{2}+2)</math> ...

In seven-dimensional [[geometry]], a '''cantellated 7-simplex''' is a convex [[uniform 7-polytope]], being ...nique 6 degrees of cantellation for the 7-simplex, including [[truncation (geometry)|truncation]]s. ...