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Polytope of Type {2,4,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12,6}*1152c
if this polytope has a name.
Group : SmallGroup(1152,134267)
Rank : 5
Schlafli Type : {2,4,12,6}
Number of vertices, edges, etc : 2, 4, 24, 36, 6
Order of s0s1s2s3s4 : 12
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 : {2,2,12,6}*576c, {2,4,6,6}*576c
   3-fold quotients : {2,4,4,6}*384
   4-fold quotients : {2,4,6,3}*288, {2,2,6,6}*288b
   6-fold quotients : {2,2,4,6}*192a, {2,4,2,6}*192
   8-fold quotients : {2,2,6,3}*144
   9-fold quotients : {2,4,4,2}*128
   12-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96
   18-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
   24-fold quotients : {2,2,2,3}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3, 75)(  4, 76)(  5, 77)(  6, 78)(  7, 79)(  8, 80)(  9, 81)( 10, 82)
( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)
( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25, 97)( 26, 98)
( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)( 34,106)
( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)( 41,113)( 42,114)
( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)( 49,121)( 50,122)
( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)( 57,129)( 58,130)
( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)( 65,137)( 66,138)
( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)( 73,145)( 74,146);;
s2 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 39, 57)( 40, 59)( 41, 58)( 42, 60)
( 43, 62)( 44, 61)( 45, 63)( 46, 65)( 47, 64)( 48, 66)( 49, 68)( 50, 67)
( 51, 69)( 52, 71)( 53, 70)( 54, 72)( 55, 74)( 56, 73)( 75, 84)( 76, 86)
( 77, 85)( 78, 87)( 79, 89)( 80, 88)( 81, 90)( 82, 92)( 83, 91)( 93,102)
( 94,104)( 95,103)( 96,105)( 97,107)( 98,106)( 99,108)(100,110)(101,109)
(111,138)(112,140)(113,139)(114,141)(115,143)(116,142)(117,144)(118,146)
(119,145)(120,129)(121,131)(122,130)(123,132)(124,134)(125,133)(126,135)
(127,137)(128,136);;
s3 := (  3, 40)(  4, 39)(  5, 41)(  6, 46)(  7, 45)(  8, 47)(  9, 43)( 10, 42)
( 11, 44)( 12, 49)( 13, 48)( 14, 50)( 15, 55)( 16, 54)( 17, 56)( 18, 52)
( 19, 51)( 20, 53)( 21, 58)( 22, 57)( 23, 59)( 24, 64)( 25, 63)( 26, 65)
( 27, 61)( 28, 60)( 29, 62)( 30, 67)( 31, 66)( 32, 68)( 33, 73)( 34, 72)
( 35, 74)( 36, 70)( 37, 69)( 38, 71)( 75,112)( 76,111)( 77,113)( 78,118)
( 79,117)( 80,119)( 81,115)( 82,114)( 83,116)( 84,121)( 85,120)( 86,122)
( 87,127)( 88,126)( 89,128)( 90,124)( 91,123)( 92,125)( 93,130)( 94,129)
( 95,131)( 96,136)( 97,135)( 98,137)( 99,133)(100,132)(101,134)(102,139)
(103,138)(104,140)(105,145)(106,144)(107,146)(108,142)(109,141)(110,143);;
s4 := (  3,  6)(  4,  8)(  5,  7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)( 19, 20)
( 21, 24)( 22, 26)( 23, 25)( 28, 29)( 30, 33)( 31, 35)( 32, 34)( 37, 38)
( 39, 42)( 40, 44)( 41, 43)( 46, 47)( 48, 51)( 49, 53)( 50, 52)( 55, 56)
( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)( 67, 71)( 68, 70)( 73, 74)
( 75, 78)( 76, 80)( 77, 79)( 82, 83)( 84, 87)( 85, 89)( 86, 88)( 91, 92)
( 93, 96)( 94, 98)( 95, 97)(100,101)(102,105)(103,107)(104,106)(109,110)
(111,114)(112,116)(113,115)(118,119)(120,123)(121,125)(122,124)(127,128)
(129,132)(130,134)(131,133)(136,137)(138,141)(139,143)(140,142)(145,146);;
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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  3, 75)(  4, 76)(  5, 77)(  6, 78)(  7, 79)(  8, 80)(  9, 81)
( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)
( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25, 97)
( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)
( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)( 41,113)
( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)( 49,121)
( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)( 57,129)
( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)( 65,137)
( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)( 73,145)
( 74,146);
s2 := Sym(146)!(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 39, 57)( 40, 59)( 41, 58)
( 42, 60)( 43, 62)( 44, 61)( 45, 63)( 46, 65)( 47, 64)( 48, 66)( 49, 68)
( 50, 67)( 51, 69)( 52, 71)( 53, 70)( 54, 72)( 55, 74)( 56, 73)( 75, 84)
( 76, 86)( 77, 85)( 78, 87)( 79, 89)( 80, 88)( 81, 90)( 82, 92)( 83, 91)
( 93,102)( 94,104)( 95,103)( 96,105)( 97,107)( 98,106)( 99,108)(100,110)
(101,109)(111,138)(112,140)(113,139)(114,141)(115,143)(116,142)(117,144)
(118,146)(119,145)(120,129)(121,131)(122,130)(123,132)(124,134)(125,133)
(126,135)(127,137)(128,136);
s3 := Sym(146)!(  3, 40)(  4, 39)(  5, 41)(  6, 46)(  7, 45)(  8, 47)(  9, 43)
( 10, 42)( 11, 44)( 12, 49)( 13, 48)( 14, 50)( 15, 55)( 16, 54)( 17, 56)
( 18, 52)( 19, 51)( 20, 53)( 21, 58)( 22, 57)( 23, 59)( 24, 64)( 25, 63)
( 26, 65)( 27, 61)( 28, 60)( 29, 62)( 30, 67)( 31, 66)( 32, 68)( 33, 73)
( 34, 72)( 35, 74)( 36, 70)( 37, 69)( 38, 71)( 75,112)( 76,111)( 77,113)
( 78,118)( 79,117)( 80,119)( 81,115)( 82,114)( 83,116)( 84,121)( 85,120)
( 86,122)( 87,127)( 88,126)( 89,128)( 90,124)( 91,123)( 92,125)( 93,130)
( 94,129)( 95,131)( 96,136)( 97,135)( 98,137)( 99,133)(100,132)(101,134)
(102,139)(103,138)(104,140)(105,145)(106,144)(107,146)(108,142)(109,141)
(110,143);
s4 := Sym(146)!(  3,  6)(  4,  8)(  5,  7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)
( 19, 20)( 21, 24)( 22, 26)( 23, 25)( 28, 29)( 30, 33)( 31, 35)( 32, 34)
( 37, 38)( 39, 42)( 40, 44)( 41, 43)( 46, 47)( 48, 51)( 49, 53)( 50, 52)
( 55, 56)( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)( 67, 71)( 68, 70)
( 73, 74)( 75, 78)( 76, 80)( 77, 79)( 82, 83)( 84, 87)( 85, 89)( 86, 88)
( 91, 92)( 93, 96)( 94, 98)( 95, 97)(100,101)(102,105)(103,107)(104,106)
(109,110)(111,114)(112,116)(113,115)(118,119)(120,123)(121,125)(122,124)
(127,128)(129,132)(130,134)(131,133)(136,137)(138,141)(139,143)(140,142)
(145,146);
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*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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