Английская Википедия:Dodecahedral cupola

Материал из Онлайн справочника
Перейти к навигацииПерейти к поиску

Dodecahedral cupola
Файл:Dodecahedral cupola.png
Schlegel diagram
Type Polyhedral cupola
Schläfli symbol {5,3} v rr{5,3}
Cells 64 1 rr{5,3} Файл:Uniform polyhedron-53-t02.png
1 {5,3} Файл:Uniform polyhedron-53-t0.png
30 {}×{3} Файл:Triangular prism.png
12 {}×{5} Файл:Pentagonal prism.png
20 {3,3} Файл:Uniform polyhedron-33-t0.png
Faces 194 80 triangles
90 squares
24 pentagons
Edges 210
Vertices 80
Dual
Symmetry group [5,3,1], order 120
Properties convex, regular-faced

In 4-dimensional geometry, the dodecahedral cupola is a polychoron bounded by a rhombicosidodecahedron, a parallel dodecahedron, connected by 30 triangular prisms, 12 pentagonal prisms, and 20 tetrahedra.[1]

Related polytopes

The dodecahedral cupola can be sliced off from a runcinated 120-cell, on a hyperplane parallel to a dodecahedral cell. The cupola can be seen in a pentagonal centered orthogonal projection of the runcinated 120-cell:

Runcinated 120-cell
Файл:120-cell t03 H3.png
Dodecahedron
Файл:Dodecahedron H3 projection.svg
(cupola top)
Rhombicosidodecahedron
Файл:Dodecahedron t02 H3.png
(cupola base)

See also

References

Шаблон:Reflist

External links

Шаблон:Polychora-stub

  1. Convex Segmentochora Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.152 dodecahedron || rhombicosidodecahedron)