"Polytope" Example Sentences
1. The polytope can be defined as a geometric shape with flat sides.
2. The regular polytope is made up of identical regular polygons.
3. The convex polytope has each of its interior angles less than 180 degrees.
4. The dodecahedron is an example of a regular polytope in three dimensions.
5. The Schläfli symbol is used to represent the regular polytope.
6. The non-convex polytope has at least one interior angle greater than 180 degrees.
7. The face of the polytope is a flat surface that makes up the boundary of the shape.
8. The polytope is an important concept in geometry and topology.
9. The platonic solids are examples of regular polytopes in three dimensions.
10. The polytope is the generalization of the polygon and the polyhedron.
11. The Kepler–Poinsot polyhedra are examples of regular star polytopes.
12. The multi-dimensional polytope is difficult to visualize but can be understood mathematically.
13. The hypercube is a regular polytope in four dimensions.
14. The vertex of the polytope is where two or more of its faces meet.
15. The toroidal polytope is a polytope that exists on the surface of a torus.
16. The irregular polytope can have different types of faces.
17. The height of a polytope is the perpendicular distance between its opposite faces.
18. The semi-regular polytope has more than one type of regular polygon as its faces.
19. The dual polytope is formed by swapping the vertices and faces of the original polytope.
20. The truncated octahedron is an example of a semi-regular polytope.
21. The symmetry group of the polytope is the set of transformations that leave the shape unchanged.
22. The 24-cell is an example of a regular polytope in four dimensions.
23. The permutahedron is an example of a polytope that arises from permutations.
24. The tesseract is a regular polytope in four dimensions.
25. The edge of the polytope is the line segment where two faces meet.
26. The honeycomb is an example of a repeating pattern of polytopes in three dimensions.
27. The order-p simplex is an example of a polytope in p-dimensional space.
28. The uniform polytope has identical faces but can have different types of faces.
29. The compound polytope is made up of two or more polytopes glued together.
30. The hypocube is an example of a regular polytope in three dimensions.
Common Phases
1. The
polytope's facets were carefully analyzed to determine its properties;
2. The mathematicians explored the various vertices of the
polytope to understand its structure;
3. The
polytope's symmetry was observed and studied in detail;
4. A computer model was created to visualize the
polytope in four dimensions;
5. The
polytope's dual was constructed to gain further insight into its geometry.