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Polytope of Type {2,24,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97547)
Rank : 4
Schlafli Type : {2,24,12}
Number of vertices, edges, etc : 2, 24, 144, 12
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 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 : {2,24,6}*576a, {2,12,12}*576a
   3-fold quotients : {2,24,4}*384a, {2,8,12}*384a
   4-fold quotients : {2,6,12}*288a, {2,12,6}*288a
   6-fold quotients : {2,4,12}*192a, {2,12,4}*192a, {2,24,2}*192, {2,8,6}*192
   8-fold quotients : {2,6,6}*144a
   9-fold quotients : {2,8,4}*128a
   12-fold quotients : {2,2,12}*96, {2,12,2}*96, {2,4,6}*96a, {2,6,4}*96a
   18-fold quotients : {2,4,4}*64, {2,8,2}*64
   24-fold quotients : {2,2,6}*48, {2,6,2}*48
   36-fold quotients : {2,2,4}*32, {2,4,2}*32
   48-fold quotients : {2,2,3}*24, {2,3,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  6,  9)(  7, 10)(  8, 11)( 15, 18)( 16, 19)( 17, 20)( 24, 27)( 25, 28)
( 26, 29)( 33, 36)( 34, 37)( 35, 38)( 39, 48)( 40, 49)( 41, 50)( 42, 54)
( 43, 55)( 44, 56)( 45, 51)( 46, 52)( 47, 53)( 57, 66)( 58, 67)( 59, 68)
( 60, 72)( 61, 73)( 62, 74)( 63, 69)( 64, 70)( 65, 71)( 75,111)( 76,112)
( 77,113)( 78,117)( 79,118)( 80,119)( 81,114)( 82,115)( 83,116)( 84,120)
( 85,121)( 86,122)( 87,126)( 88,127)( 89,128)( 90,123)( 91,124)( 92,125)
( 93,129)( 94,130)( 95,131)( 96,135)( 97,136)( 98,137)( 99,132)(100,133)
(101,134)(102,138)(103,139)(104,140)(105,144)(106,145)(107,146)(108,141)
(109,142)(110,143);;
s2 := (  3, 78)(  4, 80)(  5, 79)(  6, 75)(  7, 77)(  8, 76)(  9, 81)( 10, 83)
( 11, 82)( 12, 87)( 13, 89)( 14, 88)( 15, 84)( 16, 86)( 17, 85)( 18, 90)
( 19, 92)( 20, 91)( 21, 96)( 22, 98)( 23, 97)( 24, 93)( 25, 95)( 26, 94)
( 27, 99)( 28,101)( 29,100)( 30,105)( 31,107)( 32,106)( 33,102)( 34,104)
( 35,103)( 36,108)( 37,110)( 38,109)( 39,123)( 40,125)( 41,124)( 42,120)
( 43,122)( 44,121)( 45,126)( 46,128)( 47,127)( 48,114)( 49,116)( 50,115)
( 51,111)( 52,113)( 53,112)( 54,117)( 55,119)( 56,118)( 57,141)( 58,143)
( 59,142)( 60,138)( 61,140)( 62,139)( 63,144)( 64,146)( 65,145)( 66,132)
( 67,134)( 68,133)( 69,129)( 70,131)( 71,130)( 72,135)( 73,137)( 74,136);;
s3 := (  3,  4)(  6,  7)(  9, 10)( 12, 13)( 15, 16)( 18, 19)( 21, 22)( 24, 25)
( 27, 28)( 30, 31)( 33, 34)( 36, 37)( 39, 40)( 42, 43)( 45, 46)( 48, 49)
( 51, 52)( 54, 55)( 57, 58)( 60, 61)( 63, 64)( 66, 67)( 69, 70)( 72, 73)
( 75, 94)( 76, 93)( 77, 95)( 78, 97)( 79, 96)( 80, 98)( 81,100)( 82, 99)
( 83,101)( 84,103)( 85,102)( 86,104)( 87,106)( 88,105)( 89,107)( 90,109)
( 91,108)( 92,110)(111,130)(112,129)(113,131)(114,133)(115,132)(116,134)
(117,136)(118,135)(119,137)(120,139)(121,138)(122,140)(123,142)(124,141)
(125,143)(126,145)(127,144)(128,146);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!(  6,  9)(  7, 10)(  8, 11)( 15, 18)( 16, 19)( 17, 20)( 24, 27)
( 25, 28)( 26, 29)( 33, 36)( 34, 37)( 35, 38)( 39, 48)( 40, 49)( 41, 50)
( 42, 54)( 43, 55)( 44, 56)( 45, 51)( 46, 52)( 47, 53)( 57, 66)( 58, 67)
( 59, 68)( 60, 72)( 61, 73)( 62, 74)( 63, 69)( 64, 70)( 65, 71)( 75,111)
( 76,112)( 77,113)( 78,117)( 79,118)( 80,119)( 81,114)( 82,115)( 83,116)
( 84,120)( 85,121)( 86,122)( 87,126)( 88,127)( 89,128)( 90,123)( 91,124)
( 92,125)( 93,129)( 94,130)( 95,131)( 96,135)( 97,136)( 98,137)( 99,132)
(100,133)(101,134)(102,138)(103,139)(104,140)(105,144)(106,145)(107,146)
(108,141)(109,142)(110,143);
s2 := Sym(146)!(  3, 78)(  4, 80)(  5, 79)(  6, 75)(  7, 77)(  8, 76)(  9, 81)
( 10, 83)( 11, 82)( 12, 87)( 13, 89)( 14, 88)( 15, 84)( 16, 86)( 17, 85)
( 18, 90)( 19, 92)( 20, 91)( 21, 96)( 22, 98)( 23, 97)( 24, 93)( 25, 95)
( 26, 94)( 27, 99)( 28,101)( 29,100)( 30,105)( 31,107)( 32,106)( 33,102)
( 34,104)( 35,103)( 36,108)( 37,110)( 38,109)( 39,123)( 40,125)( 41,124)
( 42,120)( 43,122)( 44,121)( 45,126)( 46,128)( 47,127)( 48,114)( 49,116)
( 50,115)( 51,111)( 52,113)( 53,112)( 54,117)( 55,119)( 56,118)( 57,141)
( 58,143)( 59,142)( 60,138)( 61,140)( 62,139)( 63,144)( 64,146)( 65,145)
( 66,132)( 67,134)( 68,133)( 69,129)( 70,131)( 71,130)( 72,135)( 73,137)
( 74,136);
s3 := Sym(146)!(  3,  4)(  6,  7)(  9, 10)( 12, 13)( 15, 16)( 18, 19)( 21, 22)
( 24, 25)( 27, 28)( 30, 31)( 33, 34)( 36, 37)( 39, 40)( 42, 43)( 45, 46)
( 48, 49)( 51, 52)( 54, 55)( 57, 58)( 60, 61)( 63, 64)( 66, 67)( 69, 70)
( 72, 73)( 75, 94)( 76, 93)( 77, 95)( 78, 97)( 79, 96)( 80, 98)( 81,100)
( 82, 99)( 83,101)( 84,103)( 85,102)( 86,104)( 87,106)( 88,105)( 89,107)
( 90,109)( 91,108)( 92,110)(111,130)(112,129)(113,131)(114,133)(115,132)
(116,134)(117,136)(118,135)(119,137)(120,139)(121,138)(122,140)(123,142)
(124,141)(125,143)(126,145)(127,144)(128,146);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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