Polytope of Type {2,6,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {2,6,12,3}
Number of vertices, edges, etc : 2, 6, 48, 24, 4
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
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 : {2,6,6,3}*576
3-fold quotients : {2,2,12,3}*384
6-fold quotients : {2,2,6,3}*192
12-fold quotients : {2,2,3,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)( 17, 25)( 18, 26)
( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)( 42, 50)
( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 65, 73)( 66, 74)
( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)
(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)(113,121)(114,122)
(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146);;
s2 := ( 3, 11)( 4, 12)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 18)( 10, 17)
( 21, 24)( 22, 23)( 25, 26)( 27, 59)( 28, 60)( 29, 64)( 30, 63)( 31, 62)
( 32, 61)( 33, 66)( 34, 65)( 35, 51)( 36, 52)( 37, 56)( 38, 55)( 39, 54)
( 40, 53)( 41, 58)( 42, 57)( 43, 67)( 44, 68)( 45, 72)( 46, 71)( 47, 70)
( 48, 69)( 49, 74)( 50, 73)( 75, 84)( 76, 83)( 77, 87)( 78, 88)( 79, 85)
( 80, 86)( 81, 89)( 82, 90)( 91, 92)( 93, 95)( 94, 96)( 99,132)(100,131)
(101,135)(102,136)(103,133)(104,134)(105,137)(106,138)(107,124)(108,123)
(109,127)(110,128)(111,125)(112,126)(113,129)(114,130)(115,140)(116,139)
(117,143)(118,144)(119,141)(120,142)(121,145)(122,146);;
s3 := ( 3, 99)( 4,100)( 5,102)( 6,101)( 7,105)( 8,106)( 9,103)( 10,104)
( 11,107)( 12,108)( 13,110)( 14,109)( 15,113)( 16,114)( 17,111)( 18,112)
( 19,115)( 20,116)( 21,118)( 22,117)( 23,121)( 24,122)( 25,119)( 26,120)
( 27, 75)( 28, 76)( 29, 78)( 30, 77)( 31, 81)( 32, 82)( 33, 79)( 34, 80)
( 35, 83)( 36, 84)( 37, 86)( 38, 85)( 39, 89)( 40, 90)( 41, 87)( 42, 88)
( 43, 91)( 44, 92)( 45, 94)( 46, 93)( 47, 97)( 48, 98)( 49, 95)( 50, 96)
( 51,123)( 52,124)( 53,126)( 54,125)( 55,129)( 56,130)( 57,127)( 58,128)
( 59,131)( 60,132)( 61,134)( 62,133)( 63,137)( 64,138)( 65,135)( 66,136)
( 67,139)( 68,140)( 69,142)( 70,141)( 71,145)( 72,146)( 73,143)( 74,144);;
s4 := ( 3, 82)( 4, 81)( 5, 78)( 6, 77)( 7, 79)( 8, 80)( 9, 76)( 10, 75)
( 11, 90)( 12, 89)( 13, 86)( 14, 85)( 15, 87)( 16, 88)( 17, 84)( 18, 83)
( 19, 98)( 20, 97)( 21, 94)( 22, 93)( 23, 95)( 24, 96)( 25, 92)( 26, 91)
( 27,130)( 28,129)( 29,126)( 30,125)( 31,127)( 32,128)( 33,124)( 34,123)
( 35,138)( 36,137)( 37,134)( 38,133)( 39,135)( 40,136)( 41,132)( 42,131)
( 43,146)( 44,145)( 45,142)( 46,141)( 47,143)( 48,144)( 49,140)( 50,139)
( 51,106)( 52,105)( 53,102)( 54,101)( 55,103)( 56,104)( 57,100)( 58, 99)
( 59,114)( 60,113)( 61,110)( 62,109)( 63,111)( 64,112)( 65,108)( 66,107)
( 67,122)( 68,121)( 69,118)( 70,117)( 71,119)( 72,120)( 73,116)( 74,115);;
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*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)( 17, 25)
( 18, 26)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)
( 42, 50)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 65, 73)
( 66, 74)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)
( 90, 98)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)(113,121)
(114,122)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)
(138,146);
s2 := Sym(146)!( 3, 11)( 4, 12)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 18)
( 10, 17)( 21, 24)( 22, 23)( 25, 26)( 27, 59)( 28, 60)( 29, 64)( 30, 63)
( 31, 62)( 32, 61)( 33, 66)( 34, 65)( 35, 51)( 36, 52)( 37, 56)( 38, 55)
( 39, 54)( 40, 53)( 41, 58)( 42, 57)( 43, 67)( 44, 68)( 45, 72)( 46, 71)
( 47, 70)( 48, 69)( 49, 74)( 50, 73)( 75, 84)( 76, 83)( 77, 87)( 78, 88)
( 79, 85)( 80, 86)( 81, 89)( 82, 90)( 91, 92)( 93, 95)( 94, 96)( 99,132)
(100,131)(101,135)(102,136)(103,133)(104,134)(105,137)(106,138)(107,124)
(108,123)(109,127)(110,128)(111,125)(112,126)(113,129)(114,130)(115,140)
(116,139)(117,143)(118,144)(119,141)(120,142)(121,145)(122,146);
s3 := Sym(146)!( 3, 99)( 4,100)( 5,102)( 6,101)( 7,105)( 8,106)( 9,103)
( 10,104)( 11,107)( 12,108)( 13,110)( 14,109)( 15,113)( 16,114)( 17,111)
( 18,112)( 19,115)( 20,116)( 21,118)( 22,117)( 23,121)( 24,122)( 25,119)
( 26,120)( 27, 75)( 28, 76)( 29, 78)( 30, 77)( 31, 81)( 32, 82)( 33, 79)
( 34, 80)( 35, 83)( 36, 84)( 37, 86)( 38, 85)( 39, 89)( 40, 90)( 41, 87)
( 42, 88)( 43, 91)( 44, 92)( 45, 94)( 46, 93)( 47, 97)( 48, 98)( 49, 95)
( 50, 96)( 51,123)( 52,124)( 53,126)( 54,125)( 55,129)( 56,130)( 57,127)
( 58,128)( 59,131)( 60,132)( 61,134)( 62,133)( 63,137)( 64,138)( 65,135)
( 66,136)( 67,139)( 68,140)( 69,142)( 70,141)( 71,145)( 72,146)( 73,143)
( 74,144);
s4 := Sym(146)!( 3, 82)( 4, 81)( 5, 78)( 6, 77)( 7, 79)( 8, 80)( 9, 76)
( 10, 75)( 11, 90)( 12, 89)( 13, 86)( 14, 85)( 15, 87)( 16, 88)( 17, 84)
( 18, 83)( 19, 98)( 20, 97)( 21, 94)( 22, 93)( 23, 95)( 24, 96)( 25, 92)
( 26, 91)( 27,130)( 28,129)( 29,126)( 30,125)( 31,127)( 32,128)( 33,124)
( 34,123)( 35,138)( 36,137)( 37,134)( 38,133)( 39,135)( 40,136)( 41,132)
( 42,131)( 43,146)( 44,145)( 45,142)( 46,141)( 47,143)( 48,144)( 49,140)
( 50,139)( 51,106)( 52,105)( 53,102)( 54,101)( 55,103)( 56,104)( 57,100)
( 58, 99)( 59,114)( 60,113)( 61,110)( 62,109)( 63,111)( 64,112)( 65,108)
( 66,107)( 67,122)( 68,121)( 69,118)( 70,117)( 71,119)( 72,120)( 73,116)
( 74,115);
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, s3*s4*s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3 >;
to this polytope