Polytope of Type {2,12,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6,4}*1152d
if this polytope has a name.
Group : SmallGroup(1152,157550)
Rank : 5
Schlafli Type : {2,12,6,4}
Number of vertices, edges, etc : 2, 12, 36, 12, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,6,4}*576d
3-fold quotients : {2,4,6,4}*384b
6-fold quotients : {2,2,6,4}*192c
12-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7, 11)( 8, 12)( 9, 13)( 10, 14)( 19, 23)( 20, 24)( 21, 25)( 22, 26)
( 31, 35)( 32, 36)( 33, 37)( 34, 38)( 43, 47)( 44, 48)( 45, 49)( 46, 50)
( 55, 59)( 56, 60)( 57, 61)( 58, 62)( 67, 71)( 68, 72)( 69, 73)( 70, 74)
( 75,111)( 76,112)( 77,113)( 78,114)( 79,119)( 80,120)( 81,121)( 82,122)
( 83,115)( 84,116)( 85,117)( 86,118)( 87,123)( 88,124)( 89,125)( 90,126)
( 91,131)( 92,132)( 93,133)( 94,134)( 95,127)( 96,128)( 97,129)( 98,130)
( 99,135)(100,136)(101,137)(102,138)(103,143)(104,144)(105,145)(106,146)
(107,139)(108,140)(109,141)(110,142);;
s2 := ( 3, 79)( 4, 81)( 5, 80)( 6, 82)( 7, 75)( 8, 77)( 9, 76)( 10, 78)
( 11, 83)( 12, 85)( 13, 84)( 14, 86)( 15,103)( 16,105)( 17,104)( 18,106)
( 19, 99)( 20,101)( 21,100)( 22,102)( 23,107)( 24,109)( 25,108)( 26,110)
( 27, 91)( 28, 93)( 29, 92)( 30, 94)( 31, 87)( 32, 89)( 33, 88)( 34, 90)
( 35, 95)( 36, 97)( 37, 96)( 38, 98)( 39,115)( 40,117)( 41,116)( 42,118)
( 43,111)( 44,113)( 45,112)( 46,114)( 47,119)( 48,121)( 49,120)( 50,122)
( 51,139)( 52,141)( 53,140)( 54,142)( 55,135)( 56,137)( 57,136)( 58,138)
( 59,143)( 60,145)( 61,144)( 62,146)( 63,127)( 64,129)( 65,128)( 66,130)
( 67,123)( 68,125)( 69,124)( 70,126)( 71,131)( 72,133)( 73,132)( 74,134);;
s3 := ( 3, 15)( 4, 16)( 5, 18)( 6, 17)( 7, 19)( 8, 20)( 9, 22)( 10, 21)
( 11, 23)( 12, 24)( 13, 26)( 14, 25)( 29, 30)( 33, 34)( 37, 38)( 39, 51)
( 40, 52)( 41, 54)( 42, 53)( 43, 55)( 44, 56)( 45, 58)( 46, 57)( 47, 59)
( 48, 60)( 49, 62)( 50, 61)( 65, 66)( 69, 70)( 73, 74)( 75, 87)( 76, 88)
( 77, 90)( 78, 89)( 79, 91)( 80, 92)( 81, 94)( 82, 93)( 83, 95)( 84, 96)
( 85, 98)( 86, 97)(101,102)(105,106)(109,110)(111,123)(112,124)(113,126)
(114,125)(115,127)(116,128)(117,130)(118,129)(119,131)(120,132)(121,134)
(122,133)(137,138)(141,142)(145,146);;
s4 := ( 3, 6)( 4, 5)( 7, 10)( 8, 9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)
( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)
( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)
( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)
( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)
( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)
( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)
(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)(128,129)
(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)(144,145);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)!(1,2);
s1 := Sym(146)!( 7, 11)( 8, 12)( 9, 13)( 10, 14)( 19, 23)( 20, 24)( 21, 25)
( 22, 26)( 31, 35)( 32, 36)( 33, 37)( 34, 38)( 43, 47)( 44, 48)( 45, 49)
( 46, 50)( 55, 59)( 56, 60)( 57, 61)( 58, 62)( 67, 71)( 68, 72)( 69, 73)
( 70, 74)( 75,111)( 76,112)( 77,113)( 78,114)( 79,119)( 80,120)( 81,121)
( 82,122)( 83,115)( 84,116)( 85,117)( 86,118)( 87,123)( 88,124)( 89,125)
( 90,126)( 91,131)( 92,132)( 93,133)( 94,134)( 95,127)( 96,128)( 97,129)
( 98,130)( 99,135)(100,136)(101,137)(102,138)(103,143)(104,144)(105,145)
(106,146)(107,139)(108,140)(109,141)(110,142);
s2 := Sym(146)!( 3, 79)( 4, 81)( 5, 80)( 6, 82)( 7, 75)( 8, 77)( 9, 76)
( 10, 78)( 11, 83)( 12, 85)( 13, 84)( 14, 86)( 15,103)( 16,105)( 17,104)
( 18,106)( 19, 99)( 20,101)( 21,100)( 22,102)( 23,107)( 24,109)( 25,108)
( 26,110)( 27, 91)( 28, 93)( 29, 92)( 30, 94)( 31, 87)( 32, 89)( 33, 88)
( 34, 90)( 35, 95)( 36, 97)( 37, 96)( 38, 98)( 39,115)( 40,117)( 41,116)
( 42,118)( 43,111)( 44,113)( 45,112)( 46,114)( 47,119)( 48,121)( 49,120)
( 50,122)( 51,139)( 52,141)( 53,140)( 54,142)( 55,135)( 56,137)( 57,136)
( 58,138)( 59,143)( 60,145)( 61,144)( 62,146)( 63,127)( 64,129)( 65,128)
( 66,130)( 67,123)( 68,125)( 69,124)( 70,126)( 71,131)( 72,133)( 73,132)
( 74,134);
s3 := Sym(146)!( 3, 15)( 4, 16)( 5, 18)( 6, 17)( 7, 19)( 8, 20)( 9, 22)
( 10, 21)( 11, 23)( 12, 24)( 13, 26)( 14, 25)( 29, 30)( 33, 34)( 37, 38)
( 39, 51)( 40, 52)( 41, 54)( 42, 53)( 43, 55)( 44, 56)( 45, 58)( 46, 57)
( 47, 59)( 48, 60)( 49, 62)( 50, 61)( 65, 66)( 69, 70)( 73, 74)( 75, 87)
( 76, 88)( 77, 90)( 78, 89)( 79, 91)( 80, 92)( 81, 94)( 82, 93)( 83, 95)
( 84, 96)( 85, 98)( 86, 97)(101,102)(105,106)(109,110)(111,123)(112,124)
(113,126)(114,125)(115,127)(116,128)(117,130)(118,129)(119,131)(120,132)
(121,134)(122,133)(137,138)(141,142)(145,146);
s4 := Sym(146)!( 3, 6)( 4, 5)( 7, 10)( 8, 9)( 11, 14)( 12, 13)( 15, 18)
( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)
( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)
( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)
( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)
( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)
( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)
(112,113)(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)
(128,129)(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)
(144,145);
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*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, s1*s2*s3*s2*s1*s2*s3*s2,
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope