Polytope of Type {6,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,99266)
Rank : 4
Schlafli Type : {6,4,12}
Number of vertices, edges, etc : 6, 24, 48, 24
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   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 : {6,4,12}*576
   3-fold quotients : {2,4,12}*384a, {6,4,4}*384a
   4-fold quotients : {6,2,12}*288, {6,4,6}*288
   6-fold quotients : {2,4,12}*192a, {6,4,4}*192
   8-fold quotients : {3,2,12}*144, {6,2,6}*144
   9-fold quotients : {2,4,4}*128
   12-fold quotients : {2,2,12}*96, {2,4,6}*96a, {6,2,4}*96, {6,4,2}*96a
   16-fold quotients : {3,2,6}*72, {6,2,3}*72
   18-fold quotients : {2,4,4}*64
   24-fold quotients : {3,2,4}*48, {2,2,6}*48, {6,2,2}*48
   32-fold quotients : {3,2,3}*36
   36-fold quotients : {2,2,4}*32, {2,4,2}*32
   48-fold quotients : {2,2,3}*24, {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 37)(  2, 42)(  3, 44)(  4, 40)(  5, 45)(  6, 38)(  7, 43)(  8, 39)
(  9, 41)( 10, 46)( 11, 51)( 12, 53)( 13, 49)( 14, 54)( 15, 47)( 16, 52)
( 17, 48)( 18, 50)( 19, 55)( 20, 60)( 21, 62)( 22, 58)( 23, 63)( 24, 56)
( 25, 61)( 26, 57)( 27, 59)( 28, 64)( 29, 69)( 30, 71)( 31, 67)( 32, 72)
( 33, 65)( 34, 70)( 35, 66)( 36, 68)( 73,109)( 74,114)( 75,116)( 76,112)
( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)( 84,125)
( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,127)( 92,132)
( 93,134)( 94,130)( 95,135)( 96,128)( 97,133)( 98,129)( 99,131)(100,136)
(101,141)(102,143)(103,139)(104,144)(105,137)(106,142)(107,138)(108,140);;
s1 := (  1, 41)(  2, 43)(  3, 39)(  4, 44)(  5, 37)(  6, 42)(  7, 38)(  8, 40)
(  9, 45)( 10, 50)( 11, 52)( 12, 48)( 13, 53)( 14, 46)( 15, 51)( 16, 47)
( 17, 49)( 18, 54)( 19, 68)( 20, 70)( 21, 66)( 22, 71)( 23, 64)( 24, 69)
( 25, 65)( 26, 67)( 27, 72)( 28, 59)( 29, 61)( 30, 57)( 31, 62)( 32, 55)
( 33, 60)( 34, 56)( 35, 58)( 36, 63)( 73,113)( 74,115)( 75,111)( 76,116)
( 77,109)( 78,114)( 79,110)( 80,112)( 81,117)( 82,122)( 83,124)( 84,120)
( 85,125)( 86,118)( 87,123)( 88,119)( 89,121)( 90,126)( 91,140)( 92,142)
( 93,138)( 94,143)( 95,136)( 96,141)( 97,137)( 98,139)( 99,144)(100,131)
(101,133)(102,129)(103,134)(104,127)(105,132)(106,128)(107,130)(108,135);;
s2 := (  1, 37)(  2, 44)(  3, 42)(  4, 43)(  5, 41)(  6, 39)(  7, 40)(  8, 38)
(  9, 45)( 10, 46)( 11, 53)( 12, 51)( 13, 52)( 14, 50)( 15, 48)( 16, 49)
( 17, 47)( 18, 54)( 19, 55)( 20, 62)( 21, 60)( 22, 61)( 23, 59)( 24, 57)
( 25, 58)( 26, 56)( 27, 63)( 28, 64)( 29, 71)( 30, 69)( 31, 70)( 32, 68)
( 33, 66)( 34, 67)( 35, 65)( 36, 72)( 73,127)( 74,134)( 75,132)( 76,133)
( 77,131)( 78,129)( 79,130)( 80,128)( 81,135)( 82,136)( 83,143)( 84,141)
( 85,142)( 86,140)( 87,138)( 88,139)( 89,137)( 90,144)( 91,109)( 92,116)
( 93,114)( 94,115)( 95,113)( 96,111)( 97,112)( 98,110)( 99,117)(100,118)
(101,125)(102,123)(103,124)(104,122)(105,120)(106,121)(107,119)(108,126);;
s3 := (  1,112)(  2,110)(  3,117)(  4,109)(  5,116)(  6,114)(  7,115)(  8,113)
(  9,111)( 10,121)( 11,119)( 12,126)( 13,118)( 14,125)( 15,123)( 16,124)
( 17,122)( 18,120)( 19,130)( 20,128)( 21,135)( 22,127)( 23,134)( 24,132)
( 25,133)( 26,131)( 27,129)( 28,139)( 29,137)( 30,144)( 31,136)( 32,143)
( 33,141)( 34,142)( 35,140)( 36,138)( 37, 76)( 38, 74)( 39, 81)( 40, 73)
( 41, 80)( 42, 78)( 43, 79)( 44, 77)( 45, 75)( 46, 85)( 47, 83)( 48, 90)
( 49, 82)( 50, 89)( 51, 87)( 52, 88)( 53, 86)( 54, 84)( 55, 94)( 56, 92)
( 57, 99)( 58, 91)( 59, 98)( 60, 96)( 61, 97)( 62, 95)( 63, 93)( 64,103)
( 65,101)( 66,108)( 67,100)( 68,107)( 69,105)( 70,106)( 71,104)( 72,102);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*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(144)!(  1, 37)(  2, 42)(  3, 44)(  4, 40)(  5, 45)(  6, 38)(  7, 43)
(  8, 39)(  9, 41)( 10, 46)( 11, 51)( 12, 53)( 13, 49)( 14, 54)( 15, 47)
( 16, 52)( 17, 48)( 18, 50)( 19, 55)( 20, 60)( 21, 62)( 22, 58)( 23, 63)
( 24, 56)( 25, 61)( 26, 57)( 27, 59)( 28, 64)( 29, 69)( 30, 71)( 31, 67)
( 32, 72)( 33, 65)( 34, 70)( 35, 66)( 36, 68)( 73,109)( 74,114)( 75,116)
( 76,112)( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)
( 84,125)( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,127)
( 92,132)( 93,134)( 94,130)( 95,135)( 96,128)( 97,133)( 98,129)( 99,131)
(100,136)(101,141)(102,143)(103,139)(104,144)(105,137)(106,142)(107,138)
(108,140);
s1 := Sym(144)!(  1, 41)(  2, 43)(  3, 39)(  4, 44)(  5, 37)(  6, 42)(  7, 38)
(  8, 40)(  9, 45)( 10, 50)( 11, 52)( 12, 48)( 13, 53)( 14, 46)( 15, 51)
( 16, 47)( 17, 49)( 18, 54)( 19, 68)( 20, 70)( 21, 66)( 22, 71)( 23, 64)
( 24, 69)( 25, 65)( 26, 67)( 27, 72)( 28, 59)( 29, 61)( 30, 57)( 31, 62)
( 32, 55)( 33, 60)( 34, 56)( 35, 58)( 36, 63)( 73,113)( 74,115)( 75,111)
( 76,116)( 77,109)( 78,114)( 79,110)( 80,112)( 81,117)( 82,122)( 83,124)
( 84,120)( 85,125)( 86,118)( 87,123)( 88,119)( 89,121)( 90,126)( 91,140)
( 92,142)( 93,138)( 94,143)( 95,136)( 96,141)( 97,137)( 98,139)( 99,144)
(100,131)(101,133)(102,129)(103,134)(104,127)(105,132)(106,128)(107,130)
(108,135);
s2 := Sym(144)!(  1, 37)(  2, 44)(  3, 42)(  4, 43)(  5, 41)(  6, 39)(  7, 40)
(  8, 38)(  9, 45)( 10, 46)( 11, 53)( 12, 51)( 13, 52)( 14, 50)( 15, 48)
( 16, 49)( 17, 47)( 18, 54)( 19, 55)( 20, 62)( 21, 60)( 22, 61)( 23, 59)
( 24, 57)( 25, 58)( 26, 56)( 27, 63)( 28, 64)( 29, 71)( 30, 69)( 31, 70)
( 32, 68)( 33, 66)( 34, 67)( 35, 65)( 36, 72)( 73,127)( 74,134)( 75,132)
( 76,133)( 77,131)( 78,129)( 79,130)( 80,128)( 81,135)( 82,136)( 83,143)
( 84,141)( 85,142)( 86,140)( 87,138)( 88,139)( 89,137)( 90,144)( 91,109)
( 92,116)( 93,114)( 94,115)( 95,113)( 96,111)( 97,112)( 98,110)( 99,117)
(100,118)(101,125)(102,123)(103,124)(104,122)(105,120)(106,121)(107,119)
(108,126);
s3 := Sym(144)!(  1,112)(  2,110)(  3,117)(  4,109)(  5,116)(  6,114)(  7,115)
(  8,113)(  9,111)( 10,121)( 11,119)( 12,126)( 13,118)( 14,125)( 15,123)
( 16,124)( 17,122)( 18,120)( 19,130)( 20,128)( 21,135)( 22,127)( 23,134)
( 24,132)( 25,133)( 26,131)( 27,129)( 28,139)( 29,137)( 30,144)( 31,136)
( 32,143)( 33,141)( 34,142)( 35,140)( 36,138)( 37, 76)( 38, 74)( 39, 81)
( 40, 73)( 41, 80)( 42, 78)( 43, 79)( 44, 77)( 45, 75)( 46, 85)( 47, 83)
( 48, 90)( 49, 82)( 50, 89)( 51, 87)( 52, 88)( 53, 86)( 54, 84)( 55, 94)
( 56, 92)( 57, 99)( 58, 91)( 59, 98)( 60, 96)( 61, 97)( 62, 95)( 63, 93)
( 64,103)( 65,101)( 66,108)( 67,100)( 68,107)( 69,105)( 70,106)( 71,104)
( 72,102);
poly := sub<Sym(144)|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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*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 >; 
 
References : None.
to this polytope