Overview
- Group
- SmallGroup(1152,98805)
- Rank
- 4
- Schläfli Type
- {12,24,2}
- Vertices, edges, …
- 12, 144, 24, 2
- 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 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 19, 28)( 20, 30)( 21, 29)( 22, 34)( 23, 36)( 24, 35)( 25, 31)( 26, 33)( 27, 32)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)( 43, 49)( 44, 51)( 45, 50)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 65, 66)( 67, 70)( 68, 72)( 69, 71)( 73,127)( 74,129)( 75,128)( 76,133)( 77,135)( 78,134)( 79,130)( 80,132)( 81,131)( 82,136)( 83,138)( 84,137)( 85,142)( 86,144)( 87,143)( 88,139)( 89,141)( 90,140)( 91,109)( 92,111)( 93,110)( 94,115)( 95,117)( 96,116)( 97,112)( 98,114)( 99,113)(100,118)(101,120)(102,119)(103,124)(104,126)(105,125)(106,121)(107,123)(108,122);; s1 := ( 1, 77)( 2, 76)( 3, 78)( 4, 74)( 5, 73)( 6, 75)( 7, 80)( 8, 79)( 9, 81)( 10, 86)( 11, 85)( 12, 87)( 13, 83)( 14, 82)( 15, 84)( 16, 89)( 17, 88)( 18, 90)( 19,104)( 20,103)( 21,105)( 22,101)( 23,100)( 24,102)( 25,107)( 26,106)( 27,108)( 28, 95)( 29, 94)( 30, 96)( 31, 92)( 32, 91)( 33, 93)( 34, 98)( 35, 97)( 36, 99)( 37,122)( 38,121)( 39,123)( 40,119)( 41,118)( 42,120)( 43,125)( 44,124)( 45,126)( 46,113)( 47,112)( 48,114)( 49,110)( 50,109)( 51,111)( 52,116)( 53,115)( 54,117)( 55,131)( 56,130)( 57,132)( 58,128)( 59,127)( 60,129)( 61,134)( 62,133)( 63,135)( 64,140)( 65,139)( 66,141)( 67,137)( 68,136)( 69,138)( 70,143)( 71,142)( 72,144);; s2 := ( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 19, 28)( 20, 30)( 21, 29)( 22, 31)( 23, 33)( 24, 32)( 25, 34)( 26, 36)( 27, 35)( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 50, 51)( 53, 54)( 55, 64)( 56, 66)( 57, 65)( 58, 67)( 59, 69)( 60, 68)( 61, 70)( 62, 72)( 63, 71)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)( 78, 95)( 79, 97)( 80, 99)( 81, 98)( 82,100)( 83,102)( 84,101)( 85,103)( 86,105)( 87,104)( 88,106)( 89,108)( 90,107)(109,127)(110,129)(111,128)(112,130)(113,132)(114,131)(115,133)(116,135)(117,134)(118,136)(119,138)(120,137)(121,139)(122,141)(123,140)(124,142)(125,144)(126,143);; 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,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(146)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 19, 28)( 20, 30)( 21, 29)( 22, 34)( 23, 36)( 24, 35)( 25, 31)( 26, 33)( 27, 32)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)( 43, 49)( 44, 51)( 45, 50)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 65, 66)( 67, 70)( 68, 72)( 69, 71)( 73,127)( 74,129)( 75,128)( 76,133)( 77,135)( 78,134)( 79,130)( 80,132)( 81,131)( 82,136)( 83,138)( 84,137)( 85,142)( 86,144)( 87,143)( 88,139)( 89,141)( 90,140)( 91,109)( 92,111)( 93,110)( 94,115)( 95,117)( 96,116)( 97,112)( 98,114)( 99,113)(100,118)(101,120)(102,119)(103,124)(104,126)(105,125)(106,121)(107,123)(108,122); s1 := Sym(146)!( 1, 77)( 2, 76)( 3, 78)( 4, 74)( 5, 73)( 6, 75)( 7, 80)( 8, 79)( 9, 81)( 10, 86)( 11, 85)( 12, 87)( 13, 83)( 14, 82)( 15, 84)( 16, 89)( 17, 88)( 18, 90)( 19,104)( 20,103)( 21,105)( 22,101)( 23,100)( 24,102)( 25,107)( 26,106)( 27,108)( 28, 95)( 29, 94)( 30, 96)( 31, 92)( 32, 91)( 33, 93)( 34, 98)( 35, 97)( 36, 99)( 37,122)( 38,121)( 39,123)( 40,119)( 41,118)( 42,120)( 43,125)( 44,124)( 45,126)( 46,113)( 47,112)( 48,114)( 49,110)( 50,109)( 51,111)( 52,116)( 53,115)( 54,117)( 55,131)( 56,130)( 57,132)( 58,128)( 59,127)( 60,129)( 61,134)( 62,133)( 63,135)( 64,140)( 65,139)( 66,141)( 67,137)( 68,136)( 69,138)( 70,143)( 71,142)( 72,144); s2 := Sym(146)!( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 19, 28)( 20, 30)( 21, 29)( 22, 31)( 23, 33)( 24, 32)( 25, 34)( 26, 36)( 27, 35)( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 50, 51)( 53, 54)( 55, 64)( 56, 66)( 57, 65)( 58, 67)( 59, 69)( 60, 68)( 61, 70)( 62, 72)( 63, 71)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)( 78, 95)( 79, 97)( 80, 99)( 81, 98)( 82,100)( 83,102)( 84,101)( 85,103)( 86,105)( 87,104)( 88,106)( 89,108)( 90,107)(109,127)(110,129)(111,128)(112,130)(113,132)(114,131)(115,133)(116,135)(117,134)(118,136)(119,138)(120,137)(121,139)(122,141)(123,140)(124,142)(125,144)(126,143); 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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;