Overview
- Group
- SmallGroup(1152,32552)
- Rank
- 3
- Schläfli Type
- {8,4}
- Vertices, edges, …
- 144, 288, 72
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
9-fold
16-fold
18-fold
36-fold
72-fold
144-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<s0*(s1*s0*s2)^3*s1*s2> of order 3
24 facets
- 24 of {8}*16
48 vertex figures
- 48 of {4}*8
P/N, where N=<s0*(s1*s0*s2)^5*s1*s2, (s0*s2*s1)^6> of order 4
18 facets
- 18 of {8}*16
36 vertex figures
- 36 of {4}*8
P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1> of order 4
18 facets
- 18 of {8}*16
36 vertex figures
- 36 of {4}*8
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2*s2*s1*s0> of order 4
18 facets
- 18 of {8}*16
36 vertex figures
- 36 of {4}*8
P/N, where N=<s1*s0*(s1*(s2*s1*s0)^2)^2*s2*s1*s2> of order 4
18 facets
- 18 of {8}*16
36 vertex figures
- 36 of {4}*8
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2> of order 6
12 facets
- 12 of {8}*16
24 vertex figures
- 24 of {4}*8
P/N, where N=<s0*(s1*s0*s2)^3*s1*s2, s0*s1*(s2*s1*s0)^3*s1*(s2*s1*s0)^2*s2*s1> of order 6
12 facets
- 12 of {8}*16
24 vertex figures
- 24 of {4}*8
P/N, where N=<s0*(s1*s0*s2)^3*s1*s2, (s0*s2*s1)^6> of order 6
12 facets
- 12 of {8}*16
24 vertex figures
- 24 of {4}*8
P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2> of order 6
12 facets
- 12 of {8}*16
24 vertex figures
- 24 of {4}*8
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2> of order 12
6 facets
- 6 of {8}*16
12 vertex figures
- 12 of {4}*8
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2> of order 12
6 facets
- 6 of {8}*16
12 vertex figures
- 12 of {4}*8
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1> of order 12
6 facets
- 6 of {8}*16
12 vertex figures
- 12 of {4}*8
P/N, where N=<(s0*s2*s1)^3, s0*(s1*s0*s2)^3*s1*s2> of order 12
6 facets
- 6 of {8}*16
12 vertex figures
- 12 of {4}*8
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2> of order 12
6 facets
- 6 of {8}*16
12 vertex figures
- 12 of {4}*8
P/N, where N=<(s0*s2*s1)^2*s0*s1*s2*s1> of order 12
6 facets
- 6 of {8}*16
12 vertex figures
- 12 of {4}*8
Representations
Permutation Representation (GAP)
s0 := ( 1, 73)( 2, 74)( 3, 75)( 4, 81)( 5, 79)( 6, 80)( 7, 77)( 8, 78)( 9, 76)( 10, 82)( 11, 83)( 12, 84)( 13, 90)( 14, 88)( 15, 89)( 16, 86)( 17, 87)( 18, 85)( 19, 91)( 20, 92)( 21, 93)( 22, 99)( 23, 97)( 24, 98)( 25, 95)( 26, 96)( 27, 94)( 28,100)( 29,101)( 30,102)( 31,108)( 32,106)( 33,107)( 34,104)( 35,105)( 36,103)( 37,136)( 38,137)( 39,138)( 40,144)( 41,142)( 42,143)( 43,140)( 44,141)( 45,139)( 46,127)( 47,128)( 48,129)( 49,135)( 50,133)( 51,134)( 52,131)( 53,132)( 54,130)( 55,118)( 56,119)( 57,120)( 58,126)( 59,124)( 60,125)( 61,122)( 62,123)( 63,121)( 64,109)( 65,110)( 66,111)( 67,117)( 68,115)( 69,116)( 70,113)( 71,114)( 72,112);; s1 := ( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 19, 28)( 20, 33)( 21, 35)( 22, 31)( 23, 36)( 24, 29)( 25, 34)( 26, 30)( 27, 32)( 38, 42)( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 55, 64)( 56, 69)( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73,109)( 74,114)( 75,116)( 76,112)( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)( 84,125)( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,136)( 92,141)( 93,143)( 94,139)( 95,144)( 96,137)( 97,142)( 98,138)( 99,140)(100,127)(101,132)(102,134)(103,130)(104,135)(105,128)(106,133)(107,129)(108,131);; s2 := ( 1, 74)( 2, 73)( 3, 75)( 4, 78)( 5, 77)( 6, 76)( 7, 79)( 8, 81)( 9, 80)( 10, 83)( 11, 82)( 12, 84)( 13, 87)( 14, 86)( 15, 85)( 16, 88)( 17, 90)( 18, 89)( 19, 92)( 20, 91)( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 97)( 26, 99)( 27, 98)( 28,101)( 29,100)( 30,102)( 31,105)( 32,104)( 33,103)( 34,106)( 35,108)( 36,107)( 37,110)( 38,109)( 39,111)( 40,114)( 41,113)( 42,112)( 43,115)( 44,117)( 45,116)( 46,119)( 47,118)( 48,120)( 49,123)( 50,122)( 51,121)( 52,124)( 53,126)( 54,125)( 55,128)( 56,127)( 57,129)( 58,132)( 59,131)( 60,130)( 61,133)( 62,135)( 63,134)( 64,137)( 65,136)( 66,138)( 67,141)( 68,140)( 69,139)( 70,142)( 71,144)( 72,143);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(144)!( 1, 73)( 2, 74)( 3, 75)( 4, 81)( 5, 79)( 6, 80)( 7, 77)( 8, 78)( 9, 76)( 10, 82)( 11, 83)( 12, 84)( 13, 90)( 14, 88)( 15, 89)( 16, 86)( 17, 87)( 18, 85)( 19, 91)( 20, 92)( 21, 93)( 22, 99)( 23, 97)( 24, 98)( 25, 95)( 26, 96)( 27, 94)( 28,100)( 29,101)( 30,102)( 31,108)( 32,106)( 33,107)( 34,104)( 35,105)( 36,103)( 37,136)( 38,137)( 39,138)( 40,144)( 41,142)( 42,143)( 43,140)( 44,141)( 45,139)( 46,127)( 47,128)( 48,129)( 49,135)( 50,133)( 51,134)( 52,131)( 53,132)( 54,130)( 55,118)( 56,119)( 57,120)( 58,126)( 59,124)( 60,125)( 61,122)( 62,123)( 63,121)( 64,109)( 65,110)( 66,111)( 67,117)( 68,115)( 69,116)( 70,113)( 71,114)( 72,112); s1 := Sym(144)!( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 19, 28)( 20, 33)( 21, 35)( 22, 31)( 23, 36)( 24, 29)( 25, 34)( 26, 30)( 27, 32)( 38, 42)( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 55, 64)( 56, 69)( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73,109)( 74,114)( 75,116)( 76,112)( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)( 84,125)( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,136)( 92,141)( 93,143)( 94,139)( 95,144)( 96,137)( 97,142)( 98,138)( 99,140)(100,127)(101,132)(102,134)(103,130)(104,135)(105,128)(106,133)(107,129)(108,131); s2 := Sym(144)!( 1, 74)( 2, 73)( 3, 75)( 4, 78)( 5, 77)( 6, 76)( 7, 79)( 8, 81)( 9, 80)( 10, 83)( 11, 82)( 12, 84)( 13, 87)( 14, 86)( 15, 85)( 16, 88)( 17, 90)( 18, 89)( 19, 92)( 20, 91)( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 97)( 26, 99)( 27, 98)( 28,101)( 29,100)( 30,102)( 31,105)( 32,104)( 33,103)( 34,106)( 35,108)( 36,107)( 37,110)( 38,109)( 39,111)( 40,114)( 41,113)( 42,112)( 43,115)( 44,117)( 45,116)( 46,119)( 47,118)( 48,120)( 49,123)( 50,122)( 51,121)( 52,124)( 53,126)( 54,125)( 55,128)( 56,127)( 57,129)( 58,132)( 59,131)( 60,130)( 61,133)( 62,135)( 63,134)( 64,137)( 65,136)( 66,138)( 67,141)( 68,140)( 69,139)( 70,142)( 71,144)( 72,143); poly := sub<Sym(144)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.