Overview
- Group
- SmallGroup(1152,155413)
- Rank
- 5
- Schläfli Type
- {2,8,9,2}
- Vertices, edges, …
- 2, 16, 72, 18, 2
- Order of s0s1s2s3s4
- 36
- 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 := (1,2);; s1 := ( 3, 77)( 4, 78)( 5, 76)( 6, 75)( 7, 81)( 8, 82)( 9, 80)( 10, 79)( 11, 85)( 12, 86)( 13, 84)( 14, 83)( 15, 89)( 16, 90)( 17, 88)( 18, 87)( 19, 93)( 20, 94)( 21, 92)( 22, 91)( 23, 97)( 24, 98)( 25, 96)( 26, 95)( 27,101)( 28,102)( 29,100)( 30, 99)( 31,105)( 32,106)( 33,104)( 34,103)( 35,109)( 36,110)( 37,108)( 38,107)( 39,113)( 40,114)( 41,112)( 42,111)( 43,117)( 44,118)( 45,116)( 46,115)( 47,121)( 48,122)( 49,120)( 50,119)( 51,125)( 52,126)( 53,124)( 54,123)( 55,129)( 56,130)( 57,128)( 58,127)( 59,133)( 60,134)( 61,132)( 62,131)( 63,137)( 64,138)( 65,136)( 66,135)( 67,141)( 68,142)( 69,140)( 70,139)( 71,145)( 72,146)( 73,144)( 74,143);; s2 := ( 5, 7)( 6, 8)( 9, 10)( 11, 19)( 12, 20)( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 17, 26)( 18, 25)( 27, 59)( 28, 60)( 29, 63)( 30, 64)( 31, 61)( 32, 62)( 33, 66)( 34, 65)( 35, 51)( 36, 52)( 37, 55)( 38, 56)( 39, 53)( 40, 54)( 41, 58)( 42, 57)( 43, 67)( 44, 68)( 45, 71)( 46, 72)( 47, 69)( 48, 70)( 49, 74)( 50, 73)( 75, 76)( 77, 80)( 78, 79)( 83, 92)( 84, 91)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 97)( 90, 98)( 99,132)(100,131)(101,136)(102,135)(103,134)(104,133)(105,137)(106,138)(107,124)(108,123)(109,128)(110,127)(111,126)(112,125)(113,129)(114,130)(115,140)(116,139)(117,144)(118,143)(119,142)(120,141)(121,145)(122,146);; s3 := ( 3, 27)( 4, 28)( 5, 30)( 6, 29)( 7, 33)( 8, 34)( 9, 31)( 10, 32)( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 49)( 16, 50)( 17, 47)( 18, 48)( 19, 35)( 20, 36)( 21, 38)( 22, 37)( 23, 41)( 24, 42)( 25, 39)( 26, 40)( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 55, 65)( 56, 66)( 57, 63)( 58, 64)( 69, 70)( 71, 73)( 72, 74)( 75,100)( 76, 99)( 77,101)( 78,102)( 79,106)( 80,105)( 81,104)( 82,103)( 83,116)( 84,115)( 85,117)( 86,118)( 87,122)( 88,121)( 89,120)( 90,119)( 91,108)( 92,107)( 93,109)( 94,110)( 95,114)( 96,113)( 97,112)( 98,111)(123,132)(124,131)(125,133)(126,134)(127,138)(128,137)(129,136)(130,135)(139,140)(143,146)(144,145);; s4 := (147,148);; 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*s1*s0*s1,
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, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(148)!(1,2); s1 := Sym(148)!( 3, 77)( 4, 78)( 5, 76)( 6, 75)( 7, 81)( 8, 82)( 9, 80)( 10, 79)( 11, 85)( 12, 86)( 13, 84)( 14, 83)( 15, 89)( 16, 90)( 17, 88)( 18, 87)( 19, 93)( 20, 94)( 21, 92)( 22, 91)( 23, 97)( 24, 98)( 25, 96)( 26, 95)( 27,101)( 28,102)( 29,100)( 30, 99)( 31,105)( 32,106)( 33,104)( 34,103)( 35,109)( 36,110)( 37,108)( 38,107)( 39,113)( 40,114)( 41,112)( 42,111)( 43,117)( 44,118)( 45,116)( 46,115)( 47,121)( 48,122)( 49,120)( 50,119)( 51,125)( 52,126)( 53,124)( 54,123)( 55,129)( 56,130)( 57,128)( 58,127)( 59,133)( 60,134)( 61,132)( 62,131)( 63,137)( 64,138)( 65,136)( 66,135)( 67,141)( 68,142)( 69,140)( 70,139)( 71,145)( 72,146)( 73,144)( 74,143); s2 := Sym(148)!( 5, 7)( 6, 8)( 9, 10)( 11, 19)( 12, 20)( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 17, 26)( 18, 25)( 27, 59)( 28, 60)( 29, 63)( 30, 64)( 31, 61)( 32, 62)( 33, 66)( 34, 65)( 35, 51)( 36, 52)( 37, 55)( 38, 56)( 39, 53)( 40, 54)( 41, 58)( 42, 57)( 43, 67)( 44, 68)( 45, 71)( 46, 72)( 47, 69)( 48, 70)( 49, 74)( 50, 73)( 75, 76)( 77, 80)( 78, 79)( 83, 92)( 84, 91)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 97)( 90, 98)( 99,132)(100,131)(101,136)(102,135)(103,134)(104,133)(105,137)(106,138)(107,124)(108,123)(109,128)(110,127)(111,126)(112,125)(113,129)(114,130)(115,140)(116,139)(117,144)(118,143)(119,142)(120,141)(121,145)(122,146); s3 := Sym(148)!( 3, 27)( 4, 28)( 5, 30)( 6, 29)( 7, 33)( 8, 34)( 9, 31)( 10, 32)( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 49)( 16, 50)( 17, 47)( 18, 48)( 19, 35)( 20, 36)( 21, 38)( 22, 37)( 23, 41)( 24, 42)( 25, 39)( 26, 40)( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 55, 65)( 56, 66)( 57, 63)( 58, 64)( 69, 70)( 71, 73)( 72, 74)( 75,100)( 76, 99)( 77,101)( 78,102)( 79,106)( 80,105)( 81,104)( 82,103)( 83,116)( 84,115)( 85,117)( 86,118)( 87,122)( 88,121)( 89,120)( 90,119)( 91,108)( 92,107)( 93,109)( 94,110)( 95,114)( 96,113)( 97,112)( 98,111)(123,132)(124,131)(125,133)(126,134)(127,138)(128,137)(129,136)(130,135)(139,140)(143,146)(144,145); s4 := Sym(148)!(147,148); poly := sub<Sym(148)|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*s1*s0*s1, 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, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;