Overview
- Group
- SmallGroup(1152,157550)
- Rank
- 4
- Schläfli Type
- {6,12,2}
- Vertices, edges, …
- 24, 144, 48, 2
- 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 := ( 2, 3)( 6, 7)( 10, 11)( 13, 25)( 14, 27)( 15, 26)( 16, 28)( 17, 29)( 18, 31)( 19, 30)( 20, 32)( 21, 33)( 22, 35)( 23, 34)( 24, 36)( 38, 39)( 42, 43)( 46, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 74, 75)( 78, 79)( 82, 83)( 85, 97)( 86, 99)( 87, 98)( 88,100)( 89,101)( 90,103)( 91,102)( 92,104)( 93,105)( 94,107)( 95,106)( 96,108)(110,111)(114,115)(118,119)(121,133)(122,135)(123,134)(124,136)(125,137)(126,139)(127,138)(128,140)(129,141)(130,143)(131,142)(132,144);; s1 := ( 1, 13)( 2, 14)( 3, 16)( 4, 15)( 5, 21)( 6, 22)( 7, 24)( 8, 23)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 37, 49)( 38, 50)( 39, 52)( 40, 51)( 41, 57)( 42, 58)( 43, 60)( 44, 59)( 45, 53)( 46, 54)( 47, 56)( 48, 55)( 63, 64)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 73,121)( 74,122)( 75,124)( 76,123)( 77,129)( 78,130)( 79,132)( 80,131)( 81,125)( 82,126)( 83,128)( 84,127)( 85,109)( 86,110)( 87,112)( 88,111)( 89,117)( 90,118)( 91,120)( 92,119)( 93,113)( 94,114)( 95,116)( 96,115)( 97,133)( 98,134)( 99,136)(100,135)(101,141)(102,142)(103,144)(104,143)(105,137)(106,138)(107,140)(108,139);; s2 := ( 1, 80)( 2, 78)( 3, 79)( 4, 77)( 5, 76)( 6, 74)( 7, 75)( 8, 73)( 9, 84)( 10, 82)( 11, 83)( 12, 81)( 13,104)( 14,102)( 15,103)( 16,101)( 17,100)( 18, 98)( 19, 99)( 20, 97)( 21,108)( 22,106)( 23,107)( 24,105)( 25, 92)( 26, 90)( 27, 91)( 28, 89)( 29, 88)( 30, 86)( 31, 87)( 32, 85)( 33, 96)( 34, 94)( 35, 95)( 36, 93)( 37,116)( 38,114)( 39,115)( 40,113)( 41,112)( 42,110)( 43,111)( 44,109)( 45,120)( 46,118)( 47,119)( 48,117)( 49,140)( 50,138)( 51,139)( 52,137)( 53,136)( 54,134)( 55,135)( 56,133)( 57,144)( 58,142)( 59,143)( 60,141)( 61,128)( 62,126)( 63,127)( 64,125)( 65,124)( 66,122)( 67,123)( 68,121)( 69,132)( 70,130)( 71,131)( 72,129);; s3 := (145,146);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(146)!( 2, 3)( 6, 7)( 10, 11)( 13, 25)( 14, 27)( 15, 26)( 16, 28)( 17, 29)( 18, 31)( 19, 30)( 20, 32)( 21, 33)( 22, 35)( 23, 34)( 24, 36)( 38, 39)( 42, 43)( 46, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 74, 75)( 78, 79)( 82, 83)( 85, 97)( 86, 99)( 87, 98)( 88,100)( 89,101)( 90,103)( 91,102)( 92,104)( 93,105)( 94,107)( 95,106)( 96,108)(110,111)(114,115)(118,119)(121,133)(122,135)(123,134)(124,136)(125,137)(126,139)(127,138)(128,140)(129,141)(130,143)(131,142)(132,144); s1 := Sym(146)!( 1, 13)( 2, 14)( 3, 16)( 4, 15)( 5, 21)( 6, 22)( 7, 24)( 8, 23)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 37, 49)( 38, 50)( 39, 52)( 40, 51)( 41, 57)( 42, 58)( 43, 60)( 44, 59)( 45, 53)( 46, 54)( 47, 56)( 48, 55)( 63, 64)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 73,121)( 74,122)( 75,124)( 76,123)( 77,129)( 78,130)( 79,132)( 80,131)( 81,125)( 82,126)( 83,128)( 84,127)( 85,109)( 86,110)( 87,112)( 88,111)( 89,117)( 90,118)( 91,120)( 92,119)( 93,113)( 94,114)( 95,116)( 96,115)( 97,133)( 98,134)( 99,136)(100,135)(101,141)(102,142)(103,144)(104,143)(105,137)(106,138)(107,140)(108,139); s2 := Sym(146)!( 1, 80)( 2, 78)( 3, 79)( 4, 77)( 5, 76)( 6, 74)( 7, 75)( 8, 73)( 9, 84)( 10, 82)( 11, 83)( 12, 81)( 13,104)( 14,102)( 15,103)( 16,101)( 17,100)( 18, 98)( 19, 99)( 20, 97)( 21,108)( 22,106)( 23,107)( 24,105)( 25, 92)( 26, 90)( 27, 91)( 28, 89)( 29, 88)( 30, 86)( 31, 87)( 32, 85)( 33, 96)( 34, 94)( 35, 95)( 36, 93)( 37,116)( 38,114)( 39,115)( 40,113)( 41,112)( 42,110)( 43,111)( 44,109)( 45,120)( 46,118)( 47,119)( 48,117)( 49,140)( 50,138)( 51,139)( 52,137)( 53,136)( 54,134)( 55,135)( 56,133)( 57,144)( 58,142)( 59,143)( 60,141)( 61,128)( 62,126)( 63,127)( 64,125)( 65,124)( 66,122)( 67,123)( 68,121)( 69,132)( 70,130)( 71,131)( 72,129); s3 := Sym(146)!(145,146); 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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;