VERTICES
1 -1 0 0 0
1 -1/2 -1/2 -1/2 -1/2
1 -1/2 -1/2 -1/2 1/2
1 -1/2 -1/2 1/2 -1/2
1 -1/2 -1/2 1/2 1/2
1 -1/2 1/2 -1/2 -1/2
1 -1/2 1/2 -1/2 1/2
1 -1/2 1/2 1/2 -1/2
1 -1/2 1/2 1/2 1/2
1 0 -1 0 0
1 0 0 -1 0
1 0 0 0 -1
1 0 0 0 1
1 0 0 1 0
1 0 1 0 0
1 1/2 -1/2 -1/2 -1/2
1 1/2 -1/2 -1/2 1/2
1 1/2 -1/2 1/2 -1/2
1 1/2 -1/2 1/2 1/2
1 1/2 1/2 -1/2 -1/2
1 1/2 1/2 -1/2 1/2
1 1/2 1/2 1/2 -1/2
1 1/2 1/2 1/2 1/2
1 1 0 0 0
FACETS
1 0 0 -1 -1
1 0 -1 0 -1
1 0 -1 -1 0
1 -1 0 0 -1
1 -1 0 -1 0
1 -1 -1 0 0
1 1 0 0 -1
1 1 0 -1 0
1 1 -1 0 0
1 0 1 0 -1
1 0 1 -1 0
1 0 0 1 -1
1 0 0 -1 1
1 0 -1 1 0
1 0 -1 0 1
1 -1 1 0 0
1 -1 0 1 0
1 -1 0 0 1
1 1 1 0 0
1 1 0 1 0
1 1 0 0 1
1 0 1 1 0
1 0 1 0 1
1 0 0 1 1
AFFINE_HULL
# 24-cell: Tue Feb 24 12:05:26 1998
DIM
4
# 24-cell: Tue Feb 24 12:05:26 1998
AMBIENT_DIM
4
# 24-cell: Tue Feb 24 12:05:26 1998
BOUNDED
# 24-cell: Tue Feb 24 12:05:26 1998
CENTERED
N_FACETS
24
VERTICES_IN_FACETS
{4 8 12 13 18 22}
{6 8 12 14 20 22}
{7 8 13 14 21 22}
{12 16 18 20 22 23}
{13 17 18 21 22 23}
{14 19 20 21 22 23}
{0 2 4 6 8 12}
{0 3 4 7 8 13}
{0 5 6 7 8 14}
{2 4 9 12 16 18}
{3 4 9 13 17 18}
{2 6 10 12 16 20}
{3 7 11 13 17 21}
{5 6 10 14 19 20}
{5 7 11 14 19 21}
{9 15 16 17 18 23}
{10 15 16 19 20 23}
{11 15 17 19 21 23}
{0 1 2 3 4 9}
{0 1 2 5 6 10}
{0 1 3 5 7 11}
{1 2 9 10 15 16}
{1 3 9 11 15 17}
{1 5 10 11 15 19}
GRAPH
{1 2 3 4 5 6 7 8}
{0 2 3 5 9 10 11 15}
{0 1 4 6 9 10 12 16}
{0 1 4 7 9 11 13 17}
{0 2 3 8 9 12 13 18}
{0 1 6 7 10 11 14 19}
{0 2 5 8 10 12 14 20}
{0 3 5 8 11 13 14 21}
{0 4 6 7 12 13 14 22}
{1 2 3 4 15 16 17 18}
{1 2 5 6 15 16 19 20}
{1 3 5 7 15 17 19 21}
{2 4 6 8 16 18 20 22}
{3 4 7 8 17 18 21 22}
{5 6 7 8 19 20 21 22}
{1 9 10 11 16 17 19 23}
{2 9 10 12 15 18 20 23}
{3 9 11 13 15 18 21 23}
{4 9 12 13 16 17 22 23}
{5 10 11 14 15 20 21 23}
{6 10 12 14 16 19 22 23}
{7 11 13 14 17 19 22 23}
{8 12 13 14 18 20 21 23}
{15 16 17 18 19 20 21 22}
DUAL_GRAPH
{1 2 3 4 6 7 9 10}
{0 2 3 5 6 8 11 13}
{0 1 4 5 7 8 12 14}
{0 1 4 5 9 11 15 16}
{0 2 3 5 10 12 15 17}
{1 2 3 4 13 14 16 17}
{0 1 7 8 9 11 18 19}
{0 2 6 8 10 12 18 20}
{1 2 6 7 13 14 19 20}
{0 3 6 10 11 15 18 21}
{0 4 7 9 12 15 18 22}
{1 3 6 9 13 16 19 21}
{2 4 7 10 14 17 20 22}
{1 5 8 11 14 16 19 23}
{2 5 8 12 13 17 20 23}
{3 4 9 10 16 17 21 22}
{3 5 11 13 15 17 21 23}
{4 5 12 14 15 16 22 23}
{6 7 9 10 19 20 21 22}
{6 8 11 13 18 20 21 23}
{7 8 12 14 18 19 22 23}
{9 11 15 16 18 19 22 23}
{10 12 15 17 18 20 21 23}
{13 14 16 17 19 20 21 22}
N_EDGES
96
F_VECTOR
24 96 96 24
F2_VECTOR
24 192 288 144
192 96 288 288
288 288 96 192
144 288 192 24
SIMPLICIALITY
2
SIMPLICITY
2
SCHLEGEL_FACET
0
VERTEX_BARYCENTER
1 0 0 0 0
DESCRIPTION
the regular 24-cell
This polytope is associated to the Coxeter group of type F4.
It has 24 facets which are regular octahedra. The 24-cell is self-dual.
FULL_DIM
SCHLEGEL_PARAMS
0 9/10
1 0 0 1/2 1/2
1 0 0 0 0
SCHLEGEL_TRANSFORM
19/9 0 0 19/18 19/18
0 1 0 0 0
0 0 1 0 0
-10/9 0 0 -1/18 -19/18
-10/9 0 0 -19/18 -1/18
N_VERTICES
24
FAR_FACE
{}
_version 1.5.1
_application polytope