polytope
1
9.9
- noun
- /ˈpɒlɪˌtoʊp/
- Specialized
- In higher dimensions, a polytope may have many more faces than a traditional three-dimensional shape.
- invariant polytope
- corresponding matrix polytope
- induced by a polytope
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Watch on YouTubeWe have to take a leap into the unknown where we say what if it was such and such like the cosmological polytope.
- We have to take a leap into the unknown where we say what if it was such and such like the cosmological polytope.
Examples
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Moreover, it can be easily shown that satisfaction of (9) for all points in Ci is guaranteed if and only if satisfaction on its 537 vertices is ensured, which results in checking invariance conditions for the vertices of our polytope.
Academic text (2010) -
A polytope is defined as a geometric object with flat sides, such as a cube or tetrahedron.
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The ray partition considered and the polytope found are similar to the one shown in Figure 3.
Academic text (2010) -
The ray partition considered and the polytope found are shown in Figure 3.
Academic text (2010) -
They were convex polytopes and the and they were also known as Voronoi regions.
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Convex and non-convex polytopes and corresponding set-induced functions
Academic text (2010) -
These features make the families of regular polygons P(N) good candidates in the search for invariant polytopes.
Academic text (2010) -
Strictly speaking, uniform partitions of the unit n-sphere cannot be achieved in the same sense as in R², since there are only a few regular polytopes in Rⁿ.
Academic text (2010) -
Researchers studied various types of polytopes to understand their properties and relationships in geometry.
How Many Dimensions
Surface Forms
Morphology
polytope = poly + tope
The prefix poly- is recognizable as 'many', but the -tope element is not a productive English word, so the specialized geometric meaning is not directly predictable for most learners.
Etymology
Polytope comes from the Greek parts poly- 'many' and -tope 'place' and is like the words polygon and polyhedron. So a polytope is a shape with many flat 'faces' — a general form of polygons and polyhedra that can exist in any number of dimensions.