Examples of 'polytopes' in a sentence
Meaning of "polytopes"
'Polytopes' are geometric figures in geometry that exist in multiple dimensions and are composed of flat sides, edges, vertices, and cells
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- plural of polytope
How to use "polytopes" in a sentence
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polytopes
This is not true of polytopes in higher dimensions.
They are topologically dual to simple polytopes.
There are no regular star polytopes in these dimensions.
Geometrically this corresponds to projections of uniform polytopes.
No other regular polytopes are possible in three dimensions.
See also the list of regular polytopes.
There are other regular polytopes in higher dimensions.
They can be described by their use in polytopes.
Some polytopes have two possible generator points.
Website presenting the mobile application polytopes.
Abstract regular polytopes remain an active area of research.
These are not always considered to be valid abstract polytopes.
Regular polytopes are classified primarily according to their dimensionality.
These are the cross polytopes or orthoplexes.
Stereographic projection is also applied to the visualization of polytopes.
See also
All order polytopes are known to be compressed.
This definition excludes chiral polytopes.
Some regular polytopes are stars.
These may be treated as infinite polytopes.
It has been proved that all polytopes have subexponential diameter.
But in higher dimensions there are no other regular polytopes.
We give a complete description of these polytopes by means of linear inequalities.
And so on to higher order elements in higher order polytopes.
The use of polytopes or fusión proteins as vaccines is well known.
Some uniqueness results for polytopes.
Two polytopes are combinatorially.
The duoprisms are proprisms formed from exactly two polytopes.
Two polytopes are called combinatorially isomorphic if their face lattices are isomorphic.
This observation has been generalised to higher dimensional dual polytopes.
Note that dual polytopes have the same symmetry group.
It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.
The measure and cross polytopes in any dimension are dual to each other.
Symmetry groups of regular polytopes.
These complex polytopes have not been systematically explored beyond a few cases.
Higher degree rectifications can be constructed for higher dimensional polytopes.
In general all single ringed uniform polytopes have a uniform truncation.
This approach is used for example in the theory of abstract polytopes.
An important question in the theory of abstract polytopes is the amalgamation problem.
Some complex polytopes which are not fully regular have also been described.
Such groups are often named by the regular polytopes they generate.
We define the associated polytopes along with a formulation for each of them.
Geometrically this corresponds to orthogonal projections of uniform polytopes and tessellations.
The registration and use of polytopes requires full acceptance of these conditions.
Polynomials positive on polytopes.
Higher order prismatic polytopes also exist as cartesian products of any two polytopes.
Their vertex figures are icosahedral pentagonal polytopes of one less dimension.
Polytopes are geometric objects which arise in combinatorial problems and problems in optimization.
The stellation process can be applied to higher dimensional polytopes as well.
Some complex polytopes can be represented as Cartesian products.
Perles used this configuration to prove the existence of irrational polytopes in higher dimensions.
