"Hexadecachoron" Example Sentences
1. The hexadecachoron is a four-dimensional geometric shape with 16 vertices.
2. The hexadecachoron is sometimes also called a 16-cell.
3. The hexadecachoron can be thought of as the 4D analogue of a octahedron in 3D space.
4. The hexadecachoron has a total of 32 triangular faces.
5. The hexadecachoron can be inscribed inside a tesseract, or 4D cube, with each vertex touching a corner of the tesseract.
6. The hexadecachoron can be dissected into 8 hyperpyramids, each with a square base.
7. The hexadecachoron belongs to a family of regular polytopes in 4D space.
8. The dual of the hexadecachoron is the tesseract.
9. The vertices of the hexadecachoron can be represented by the coordinates (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1).
10. The edges of the hexadecachoron connect pairs of vertices that are exactly two units apart.
11. The hexadecachoron is a convex polytope, meaning that it has no internal angles greater than 180 degrees.
12. The hexadecachoron was first studied by Ludwig Schläfli in the 19th century.
13. The Schläfli symbol for the hexadecachoron is {4, 3, 3}.
14. The volume of the hexadecachoron is 2^8/3 times the volume of a tetrahedron.
15. The surface area of the hexadecachoron is 4 times the surface area of a tetrahedron.
16. The hexadecachoron has 24 square faces that are perpendicular to its edges.
17. The hexadecachoron has a mirror symmetry that can be represented by the group O_h.
18. The hexadecachoron has a total of 96 edges.
19. The hexadecachoron is one of six regular polychora in 4D space.
20. The hexadecachoron can be represented in the Coxeter-Dynkin diagram as 120.
21. The hexadecachoron has a total of 32 axial ribs.
22. The hexadecachoron has automorphism group of order 384.
23. The hexadecachoron can be represented as the convex hull of its 16 vertices.
24. The set of 16 vertices of the hexadecachoron forms a three-dimensional hypertetrahedron known as the 16-cell honeycomb.
25. The hexadecachoron has 32 cells, each of which is a tetrahedron.
26. The hexadecachoron is the fourth member of the simplex family of polytopes in 4D space.
27. The hexadecachoron can be inscribed in a hypersphere of radius 1.
28. The hexadecachoron has a dihedral angle of 144 degrees.
29. The hexadecachoron is unique among regular polychora in that it has no intersecting cells.
30. The hexadecachoron can be obtained from a hypercube by adding a vertex at the center of each face.
Common Phases
1. The
hexadecachoron is a convex regular 4-polytope;
2. It has 16 cell faces that are all regular tetrahedra;
3. The
hexadecachoron has 32 triangular faces and 24 edges;
4. Its vertices are arranged in a 4-dimensional hyperdiamond shape;
5. The
hexadecachoron can be projected onto a 3-dimensional space;
6. It is also known as the 16-cell or solido octadecachoron;
7. The
hexadecachoron is one of the six regular 4-polytopes;
8. It has 24 vertices and its Schläfli symbol is {3,3,4}.
9. The
hexadecachoron has a total of 1280 edges;
10. It represents a significant manifestation of geometry in four dimensions.