Overview
- Group
- SmallGroup(1152,98805)
- Rank
- 4
- Schläfli Type
- {2,24,12}
- Vertices, edges, …
- 2, 24, 144, 12
- Order of s0s1s2s3
- 24
- 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
9-fold
12-fold
16-fold
18-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, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 21, 30)( 22, 32)( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)( 40, 41)( 43, 44)( 46, 47)( 49, 50)( 52, 53)( 55, 56)( 57, 66)( 58, 68)( 59, 67)( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 99)( 82,101)( 83,100)( 84,102)( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108)( 91,110)( 92,109)(111,129)(112,131)(113,130)(114,132)(115,134)(116,133)(117,135)(118,137)(119,136)(120,138)(121,140)(122,139)(123,141)(124,143)(125,142)(126,144)(127,146)(128,145);; s2 := ( 3, 76)( 4, 75)( 5, 77)( 6, 82)( 7, 81)( 8, 83)( 9, 79)( 10, 78)( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)( 18, 88)( 19, 87)( 20, 89)( 21,103)( 22,102)( 23,104)( 24,109)( 25,108)( 26,110)( 27,106)( 28,105)( 29,107)( 30, 94)( 31, 93)( 32, 95)( 33,100)( 34, 99)( 35,101)( 36, 97)( 37, 96)( 38, 98)( 39,121)( 40,120)( 41,122)( 42,127)( 43,126)( 44,128)( 45,124)( 46,123)( 47,125)( 48,112)( 49,111)( 50,113)( 51,118)( 52,117)( 53,119)( 54,115)( 55,114)( 56,116)( 57,130)( 58,129)( 59,131)( 60,136)( 61,135)( 62,137)( 63,133)( 64,132)( 65,134)( 66,139)( 67,138)( 68,140)( 69,145)( 70,144)( 71,146)( 72,142)( 73,141)( 74,143);; s3 := ( 3, 6)( 4, 8)( 5, 7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)( 19, 20)( 21, 33)( 22, 35)( 23, 34)( 24, 30)( 25, 32)( 26, 31)( 27, 36)( 28, 38)( 29, 37)( 39, 51)( 40, 53)( 41, 52)( 42, 48)( 43, 50)( 44, 49)( 45, 54)( 46, 56)( 47, 55)( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)( 67, 71)( 68, 70)( 73, 74)( 75,132)( 76,134)( 77,133)( 78,129)( 79,131)( 80,130)( 81,135)( 82,137)( 83,136)( 84,141)( 85,143)( 86,142)( 87,138)( 88,140)( 89,139)( 90,144)( 91,146)( 92,145)( 93,114)( 94,116)( 95,115)( 96,111)( 97,113)( 98,112)( 99,117)(100,119)(101,118)(102,123)(103,125)(104,124)(105,120)(106,122)(107,121)(108,126)(109,128)(110,127);; 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*s3*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*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(146)!(1,2); s1 := Sym(146)!( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 21, 30)( 22, 32)( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)( 40, 41)( 43, 44)( 46, 47)( 49, 50)( 52, 53)( 55, 56)( 57, 66)( 58, 68)( 59, 67)( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 99)( 82,101)( 83,100)( 84,102)( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108)( 91,110)( 92,109)(111,129)(112,131)(113,130)(114,132)(115,134)(116,133)(117,135)(118,137)(119,136)(120,138)(121,140)(122,139)(123,141)(124,143)(125,142)(126,144)(127,146)(128,145); s2 := Sym(146)!( 3, 76)( 4, 75)( 5, 77)( 6, 82)( 7, 81)( 8, 83)( 9, 79)( 10, 78)( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)( 18, 88)( 19, 87)( 20, 89)( 21,103)( 22,102)( 23,104)( 24,109)( 25,108)( 26,110)( 27,106)( 28,105)( 29,107)( 30, 94)( 31, 93)( 32, 95)( 33,100)( 34, 99)( 35,101)( 36, 97)( 37, 96)( 38, 98)( 39,121)( 40,120)( 41,122)( 42,127)( 43,126)( 44,128)( 45,124)( 46,123)( 47,125)( 48,112)( 49,111)( 50,113)( 51,118)( 52,117)( 53,119)( 54,115)( 55,114)( 56,116)( 57,130)( 58,129)( 59,131)( 60,136)( 61,135)( 62,137)( 63,133)( 64,132)( 65,134)( 66,139)( 67,138)( 68,140)( 69,145)( 70,144)( 71,146)( 72,142)( 73,141)( 74,143); s3 := Sym(146)!( 3, 6)( 4, 8)( 5, 7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)( 19, 20)( 21, 33)( 22, 35)( 23, 34)( 24, 30)( 25, 32)( 26, 31)( 27, 36)( 28, 38)( 29, 37)( 39, 51)( 40, 53)( 41, 52)( 42, 48)( 43, 50)( 44, 49)( 45, 54)( 46, 56)( 47, 55)( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)( 67, 71)( 68, 70)( 73, 74)( 75,132)( 76,134)( 77,133)( 78,129)( 79,131)( 80,130)( 81,135)( 82,137)( 83,136)( 84,141)( 85,143)( 86,142)( 87,138)( 88,140)( 89,139)( 90,144)( 91,146)( 92,145)( 93,114)( 94,116)( 95,115)( 96,111)( 97,113)( 98,112)( 99,117)(100,119)(101,118)(102,123)(103,125)(104,124)(105,120)(106,122)(107,121)(108,126)(109,128)(110,127); 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*s3*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;