Overview
- Group
- SmallGroup(1152,157640)
- Rank
- 4
- Schläfli Type
- {2,6,12}
- Vertices, edges, …
- 2, 24, 144, 48
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
16-fold
24-fold
36-fold
48-fold
72-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 15, 27)( 16, 29)( 17, 28)( 18, 30)( 19, 35)( 20, 37)( 21, 36)( 22, 38)( 23, 31)( 24, 33)( 25, 32)( 26, 34)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 71)( 56, 73)( 57, 72)( 58, 74)( 59, 67)( 60, 69)( 61, 68)( 62, 70)( 76, 77)( 79, 83)( 80, 85)( 81, 84)( 82, 86)( 87, 99)( 88,101)( 89,100)( 90,102)( 91,107)( 92,109)( 93,108)( 94,110)( 95,103)( 96,105)( 97,104)( 98,106)(112,113)(115,119)(116,121)(117,120)(118,122)(123,135)(124,137)(125,136)(126,138)(127,143)(128,145)(129,144)(130,146)(131,139)(132,141)(133,140)(134,142);; s2 := ( 3, 91)( 4, 92)( 5, 94)( 6, 93)( 7, 87)( 8, 88)( 9, 90)( 10, 89)( 11, 95)( 12, 96)( 13, 98)( 14, 97)( 15, 79)( 16, 80)( 17, 82)( 18, 81)( 19, 75)( 20, 76)( 21, 78)( 22, 77)( 23, 83)( 24, 84)( 25, 86)( 26, 85)( 27,103)( 28,104)( 29,106)( 30,105)( 31, 99)( 32,100)( 33,102)( 34,101)( 35,107)( 36,108)( 37,110)( 38,109)( 39,127)( 40,128)( 41,130)( 42,129)( 43,123)( 44,124)( 45,126)( 46,125)( 47,131)( 48,132)( 49,134)( 50,133)( 51,115)( 52,116)( 53,118)( 54,117)( 55,111)( 56,112)( 57,114)( 58,113)( 59,119)( 60,120)( 61,122)( 62,121)( 63,139)( 64,140)( 65,142)( 66,141)( 67,135)( 68,136)( 69,138)( 70,137)( 71,143)( 72,144)( 73,146)( 74,145);; s3 := ( 3, 6)( 7, 10)( 11, 14)( 15, 30)( 16, 28)( 17, 29)( 18, 27)( 19, 34)( 20, 32)( 21, 33)( 22, 31)( 23, 38)( 24, 36)( 25, 37)( 26, 35)( 39, 42)( 43, 46)( 47, 50)( 51, 66)( 52, 64)( 53, 65)( 54, 63)( 55, 70)( 56, 68)( 57, 69)( 58, 67)( 59, 74)( 60, 72)( 61, 73)( 62, 71)( 75,114)( 76,112)( 77,113)( 78,111)( 79,118)( 80,116)( 81,117)( 82,115)( 83,122)( 84,120)( 85,121)( 86,119)( 87,138)( 88,136)( 89,137)( 90,135)( 91,142)( 92,140)( 93,141)( 94,139)( 95,146)( 96,144)( 97,145)( 98,143)( 99,126)(100,124)(101,125)(102,123)(103,130)(104,128)(105,129)(106,127)(107,134)(108,132)(109,133)(110,131);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2*s3*s2*s1,
s1*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(146)!(1,2); s1 := Sym(146)!( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 15, 27)( 16, 29)( 17, 28)( 18, 30)( 19, 35)( 20, 37)( 21, 36)( 22, 38)( 23, 31)( 24, 33)( 25, 32)( 26, 34)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 71)( 56, 73)( 57, 72)( 58, 74)( 59, 67)( 60, 69)( 61, 68)( 62, 70)( 76, 77)( 79, 83)( 80, 85)( 81, 84)( 82, 86)( 87, 99)( 88,101)( 89,100)( 90,102)( 91,107)( 92,109)( 93,108)( 94,110)( 95,103)( 96,105)( 97,104)( 98,106)(112,113)(115,119)(116,121)(117,120)(118,122)(123,135)(124,137)(125,136)(126,138)(127,143)(128,145)(129,144)(130,146)(131,139)(132,141)(133,140)(134,142); s2 := Sym(146)!( 3, 91)( 4, 92)( 5, 94)( 6, 93)( 7, 87)( 8, 88)( 9, 90)( 10, 89)( 11, 95)( 12, 96)( 13, 98)( 14, 97)( 15, 79)( 16, 80)( 17, 82)( 18, 81)( 19, 75)( 20, 76)( 21, 78)( 22, 77)( 23, 83)( 24, 84)( 25, 86)( 26, 85)( 27,103)( 28,104)( 29,106)( 30,105)( 31, 99)( 32,100)( 33,102)( 34,101)( 35,107)( 36,108)( 37,110)( 38,109)( 39,127)( 40,128)( 41,130)( 42,129)( 43,123)( 44,124)( 45,126)( 46,125)( 47,131)( 48,132)( 49,134)( 50,133)( 51,115)( 52,116)( 53,118)( 54,117)( 55,111)( 56,112)( 57,114)( 58,113)( 59,119)( 60,120)( 61,122)( 62,121)( 63,139)( 64,140)( 65,142)( 66,141)( 67,135)( 68,136)( 69,138)( 70,137)( 71,143)( 72,144)( 73,146)( 74,145); s3 := Sym(146)!( 3, 6)( 7, 10)( 11, 14)( 15, 30)( 16, 28)( 17, 29)( 18, 27)( 19, 34)( 20, 32)( 21, 33)( 22, 31)( 23, 38)( 24, 36)( 25, 37)( 26, 35)( 39, 42)( 43, 46)( 47, 50)( 51, 66)( 52, 64)( 53, 65)( 54, 63)( 55, 70)( 56, 68)( 57, 69)( 58, 67)( 59, 74)( 60, 72)( 61, 73)( 62, 71)( 75,114)( 76,112)( 77,113)( 78,111)( 79,118)( 80,116)( 81,117)( 82,115)( 83,122)( 84,120)( 85,121)( 86,119)( 87,138)( 88,136)( 89,137)( 90,135)( 91,142)( 92,140)( 93,141)( 94,139)( 95,146)( 96,144)( 97,145)( 98,143)( 99,126)(100,124)(101,125)(102,123)(103,130)(104,128)(105,129)(106,127)(107,134)(108,132)(109,133)(110,131); poly := sub<Sym(146)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2*s3*s2*s1, s1*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;