Regular convex 4-polytopes | |||||||
---|---|---|---|---|---|---|---|
Symmetry group | A4 | B4 | F4 | H4 | |||
Name |
5-cell Hyper-
tetrahedron |
16-cell Hyper-
octahedron |
8-cell Hyper-
cube |
24-cell
|
600-cell Hyper-
icosahedron |
120-cell Hyper-
dodecahedron | |
SchlΓ€fli symbol | {3, 3, 3} | {3, 3, 4} | {4, 3, 3} | {3, 4, 3} | {3, 3, 5} | {5, 3, 3} | |
Coxeter mirrors | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Mirror dihedrals | π /3 π /3 π /3 π /2 π /2 π /2 | π /3 π /3 π /4 π /2 π /2 π /2 | π /4 π /3 π /3 π /2 π /2 π /2 | π /3 π /4 π /3 π /2 π /2 π /2 | π /3 π /3 π /5 π /2 π /2 π /2 | π /5 π /3 π /3 π /2 π /2 π /2 | |
Graph |
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Vertices | 5 tetrahedral | 8 octahedral | 16 tetrahedral | 24 cubical | 120 icosahedral | 600 tetrahedral | |
Edges | 10 triangular | 24 square | 32 triangular | 96 triangular | 720 pentagonal | 1200 triangular | |
Faces | 10 triangles | 32 triangles | 24 squares | 96 triangles | 1200 triangles | 720 pentagons | |
Cells | 5 tetrahedra | 16 tetrahedra | 8 cubes | 24 octahedra | 600 tetrahedra | 120 dodecahedra | |
Tori | 1 5-tetrahedron | 2 8-tetrahedron | 2 4-cube | 4 6-octahedron | 20 30-tetrahedron | 12 10-dodecahedron | |
Inscribed | 120 in 120-cell | 675 in 120-cell | 2 16-cells | 3 8-cells | 25 24-cells | 10 600-cells | |
Great polygons | 2 squares x 3 | 4 rectangles x 4 | 4 hexagons x 4 | 12 decagons x 6 | 100 irregular hexagons x 4 | ||
Petrie polygons | 1 pentagon x 2 | 1 octagon x 3 | 2 octagons x 4 | 2 dodecagons x 4 | 4 30-gons x 6 | 20 30-gons x 4 | |
Long radius | |||||||
Edge length | |||||||
Short radius | |||||||
Area | |||||||
Volume | |||||||
4-Content |
Regular convex 4-polytopes | |||||||
---|---|---|---|---|---|---|---|
Symmetry group | A4 | B4 | F4 | H4 | |||
Name |
5-cell Hyper-
tetrahedron |
16-cell Hyper-
octahedron |
8-cell Hyper-
cube |
24-cell
|
600-cell Hyper-
icosahedron |
120-cell Hyper-
dodecahedron | |
SchlΓ€fli symbol | {3, 3, 3} | {3, 3, 4} | {4, 3, 3} | {3, 4, 3} | {3, 3, 5} | {5, 3, 3} | |
Coxeter mirrors | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Mirror dihedrals | π /3 π /3 π /3 π /2 π /2 π /2 | π /3 π /3 π /4 π /2 π /2 π /2 | π /4 π /3 π /3 π /2 π /2 π /2 | π /3 π /4 π /3 π /2 π /2 π /2 | π /3 π /3 π /5 π /2 π /2 π /2 | π /5 π /3 π /3 π /2 π /2 π /2 | |
Graph |
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Vertices | 5 tetrahedral | 8 octahedral | 16 tetrahedral | 24 cubical | 120 icosahedral | 600 tetrahedral | |
Edges | 10 triangular | 24 square | 32 triangular | 96 triangular | 720 pentagonal | 1200 triangular | |
Faces | 10 triangles | 32 triangles | 24 squares | 96 triangles | 1200 triangles | 720 pentagons | |
Cells | 5 tetrahedra | 16 tetrahedra | 8 cubes | 24 octahedra | 600 tetrahedra | 120 dodecahedra | |
Tori | 1 5-tetrahedron | 2 8-tetrahedron | 2 4-cube | 4 6-octahedron | 20 30-tetrahedron | 12 10-dodecahedron | |
Inscribed | 120 in 120-cell | 675 in 120-cell | 2 16-cells | 3 8-cells | 25 24-cells | 10 600-cells | |
Great polygons | 2 squares x 3 | 4 rectangles x 4 | 4 hexagons x 4 | 12 decagons x 6 | 100 irregular hexagons x 4 | ||
Petrie polygons | 1 pentagon x 2 | 1 octagon x 3 | 2 octagons x 4 | 2 dodecagons x 4 | 4 30-gons x 6 | 20 30-gons x 4 | |
Long radius | |||||||
Edge length | |||||||
Short radius | |||||||
Area | |||||||
Volume | |||||||
4-Content |