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Rectified 24-cell : ウィキペディア英語版
Rectified 24-cell

r
|-
|bgcolor=#e7dcc3|Coxeter diagrams
|colspan=2|
or
|-
|bgcolor=#e7dcc3|Cells
|48
|24 ''3.4.3.4'' 20px
24 ''4.4.4'' 20px
|-
|bgcolor=#e7dcc3|Faces
|240
|96
144
|-
|bgcolor=#e7dcc3|Edges
|colspan=2|288
|-
|bgcolor=#e7dcc3|Vertices
|colspan=2|96
|-
|bgcolor=#e7dcc3|Vertex figure
|colspan=2|50px50px50px
Triangular prism
|-
|bgcolor=#e7dcc3|Symmetry groups
|colspan=2|F4 (), order 1152
B4 (), order 384
D4 (), order 192
|-
|bgcolor=#e7dcc3|Properties
|colspan=2|convex, edge-transitive
|-
|bgcolor=#e7dcc3|Uniform index
|colspan=2|''22'' 23 ''24''
|}
In geometry, the rectified 24-cell or rectified icositetrachoron is a uniform 4-dimensional polytope (or uniform 4-polytope), which is bounded by 48 cells: 24 cubes, and 24 cuboctahedra. It can be obtained by reducing the 24-cell's cells to cubes or cuboctahedra.
E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as tC24.
It can also be considered a cantellated 16-cell with the lower symmetries B4 = (). B4 would lead to a bicoloring of the cuboctahedral cells into 8 and 16 each. It is also called a runcicantellated demitesseract in a D4 symmetry, giving 3 colors of cells, 8 for each.
== Cartesian coordinates ==

A rectified 24-cell having an edge length of √2 has vertices given by all permutations and sign permutations of the following Cartesian coordinates:
: (0,1,1,2) (= 96 vertices )
The dual configuration with edge length 2 has all coordinate and sign permutations of:
: (0,2,2,2) (= 32 vertices )
: (1,1,1,3) (= 64 vertices )

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Rectified 24-cell」の詳細全文を読む



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