Overview
- Group
- SmallGroup(1152,157640)
- Rank
- 5
- Schläfli Type
- {3,6,4,2}
- Vertices, edges, …
- 12, 36, 48, 4, 2
- Order of s0s1s2s3s4
- 12
- Order of s0s1s2s3s4s3s2s1
- 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
24-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 9)( 6, 11)( 7, 10)( 8, 12)( 13, 25)( 14, 27)( 15, 26)( 16, 28)( 17, 33)( 18, 35)( 19, 34)( 20, 36)( 21, 29)( 22, 31)( 23, 30)( 24, 32)( 38, 39)( 41, 45)( 42, 47)( 43, 46)( 44, 48)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 69)( 54, 71)( 55, 70)( 56, 72)( 57, 65)( 58, 67)( 59, 66)( 60, 68)( 74, 75)( 77, 81)( 78, 83)( 79, 82)( 80, 84)( 85, 97)( 86, 99)( 87, 98)( 88,100)( 89,105)( 90,107)( 91,106)( 92,108)( 93,101)( 94,103)( 95,102)( 96,104)(110,111)(113,117)(114,119)(115,118)(116,120)(121,133)(122,135)(123,134)(124,136)(125,141)(126,143)(127,142)(128,144)(129,137)(130,139)(131,138)(132,140);; s1 := ( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 13)( 6, 14)( 7, 16)( 8, 15)( 9, 21)( 10, 22)( 11, 24)( 12, 23)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 49)( 42, 50)( 43, 52)( 44, 51)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 61, 65)( 62, 66)( 63, 68)( 64, 67)( 71, 72)( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 85)( 78, 86)( 79, 88)( 80, 87)( 81, 93)( 82, 94)( 83, 96)( 84, 95)( 97,101)( 98,102)( 99,104)(100,103)(107,108)(109,125)(110,126)(111,128)(112,127)(113,121)(114,122)(115,124)(116,123)(117,129)(118,130)(119,132)(120,131)(133,137)(134,138)(135,140)(136,139)(143,144);; s2 := ( 1, 4)( 5, 8)( 9, 12)( 13, 28)( 14, 26)( 15, 27)( 16, 25)( 17, 32)( 18, 30)( 19, 31)( 20, 29)( 21, 36)( 22, 34)( 23, 35)( 24, 33)( 37, 40)( 41, 44)( 45, 48)( 49, 64)( 50, 62)( 51, 63)( 52, 61)( 53, 68)( 54, 66)( 55, 67)( 56, 65)( 57, 72)( 58, 70)( 59, 71)( 60, 69)( 73,112)( 74,110)( 75,111)( 76,109)( 77,116)( 78,114)( 79,115)( 80,113)( 81,120)( 82,118)( 83,119)( 84,117)( 85,136)( 86,134)( 87,135)( 88,133)( 89,140)( 90,138)( 91,139)( 92,137)( 93,144)( 94,142)( 95,143)( 96,141)( 97,124)( 98,122)( 99,123)(100,121)(101,128)(102,126)(103,127)(104,125)(105,132)(106,130)(107,131)(108,129);; s3 := ( 1, 73)( 2, 74)( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144);; s4 := (145,146);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(146)!( 2, 3)( 5, 9)( 6, 11)( 7, 10)( 8, 12)( 13, 25)( 14, 27)( 15, 26)( 16, 28)( 17, 33)( 18, 35)( 19, 34)( 20, 36)( 21, 29)( 22, 31)( 23, 30)( 24, 32)( 38, 39)( 41, 45)( 42, 47)( 43, 46)( 44, 48)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 69)( 54, 71)( 55, 70)( 56, 72)( 57, 65)( 58, 67)( 59, 66)( 60, 68)( 74, 75)( 77, 81)( 78, 83)( 79, 82)( 80, 84)( 85, 97)( 86, 99)( 87, 98)( 88,100)( 89,105)( 90,107)( 91,106)( 92,108)( 93,101)( 94,103)( 95,102)( 96,104)(110,111)(113,117)(114,119)(115,118)(116,120)(121,133)(122,135)(123,134)(124,136)(125,141)(126,143)(127,142)(128,144)(129,137)(130,139)(131,138)(132,140); s1 := Sym(146)!( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 13)( 6, 14)( 7, 16)( 8, 15)( 9, 21)( 10, 22)( 11, 24)( 12, 23)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 49)( 42, 50)( 43, 52)( 44, 51)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 61, 65)( 62, 66)( 63, 68)( 64, 67)( 71, 72)( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 85)( 78, 86)( 79, 88)( 80, 87)( 81, 93)( 82, 94)( 83, 96)( 84, 95)( 97,101)( 98,102)( 99,104)(100,103)(107,108)(109,125)(110,126)(111,128)(112,127)(113,121)(114,122)(115,124)(116,123)(117,129)(118,130)(119,132)(120,131)(133,137)(134,138)(135,140)(136,139)(143,144); s2 := Sym(146)!( 1, 4)( 5, 8)( 9, 12)( 13, 28)( 14, 26)( 15, 27)( 16, 25)( 17, 32)( 18, 30)( 19, 31)( 20, 29)( 21, 36)( 22, 34)( 23, 35)( 24, 33)( 37, 40)( 41, 44)( 45, 48)( 49, 64)( 50, 62)( 51, 63)( 52, 61)( 53, 68)( 54, 66)( 55, 67)( 56, 65)( 57, 72)( 58, 70)( 59, 71)( 60, 69)( 73,112)( 74,110)( 75,111)( 76,109)( 77,116)( 78,114)( 79,115)( 80,113)( 81,120)( 82,118)( 83,119)( 84,117)( 85,136)( 86,134)( 87,135)( 88,133)( 89,140)( 90,138)( 91,139)( 92,137)( 93,144)( 94,142)( 95,143)( 96,141)( 97,124)( 98,122)( 99,123)(100,121)(101,128)(102,126)(103,127)(104,125)(105,132)(106,130)(107,131)(108,129); s3 := Sym(146)!( 1, 73)( 2, 74)( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144); s4 := Sym(146)!(145,146); poly := sub<Sym(146)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;