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Polytope of Type {48,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6}*576b
if this polytope has a name.
Group : SmallGroup(576,2112)
Rank : 3
Schlafli Type : {48,6}
Number of vertices, edges, etc : 48, 144, 6
Order of s0s1s2 : 48
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {48,6,2} of size 1152
   {48,6,3} of size 1728
Vertex Figure Of :
   {2,48,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,6}*288b
   3-fold quotients : {48,2}*192
   4-fold quotients : {12,6}*144b
   6-fold quotients : {24,2}*96
   8-fold quotients : {6,6}*72c
   9-fold quotients : {16,2}*64
   12-fold quotients : {12,2}*48
   16-fold quotients : {3,6}*36
   18-fold quotients : {8,2}*32
   24-fold quotients : {6,2}*24
   36-fold quotients : {4,2}*16
   48-fold quotients : {3,2}*12
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {48,12}*1152a, {96,6}*1152b
   3-fold covers : {144,6}*1728b, {48,6}*1728a, {48,6}*1728f
Permutation Representation (GAP) :
s0 := (  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 19, 28)( 20, 30)( 21, 29)( 22, 34)( 23, 36)( 24, 35)( 25, 31)( 26, 33)
( 27, 32)( 37, 55)( 38, 57)( 39, 56)( 40, 61)( 41, 63)( 42, 62)( 43, 58)
( 44, 60)( 45, 59)( 46, 64)( 47, 66)( 48, 65)( 49, 70)( 50, 72)( 51, 71)
( 52, 67)( 53, 69)( 54, 68)( 73,109)( 74,111)( 75,110)( 76,115)( 77,117)
( 78,116)( 79,112)( 80,114)( 81,113)( 82,118)( 83,120)( 84,119)( 85,124)
( 86,126)( 87,125)( 88,121)( 89,123)( 90,122)( 91,136)( 92,138)( 93,137)
( 94,142)( 95,144)( 96,143)( 97,139)( 98,141)( 99,140)(100,127)(101,129)
(102,128)(103,133)(104,135)(105,134)(106,130)(107,132)(108,131);;
s1 := (  1, 77)(  2, 76)(  3, 78)(  4, 74)(  5, 73)(  6, 75)(  7, 80)(  8, 79)
(  9, 81)( 10, 86)( 11, 85)( 12, 87)( 13, 83)( 14, 82)( 15, 84)( 16, 89)
( 17, 88)( 18, 90)( 19,104)( 20,103)( 21,105)( 22,101)( 23,100)( 24,102)
( 25,107)( 26,106)( 27,108)( 28, 95)( 29, 94)( 30, 96)( 31, 92)( 32, 91)
( 33, 93)( 34, 98)( 35, 97)( 36, 99)( 37,131)( 38,130)( 39,132)( 40,128)
( 41,127)( 42,129)( 43,134)( 44,133)( 45,135)( 46,140)( 47,139)( 48,141)
( 49,137)( 50,136)( 51,138)( 52,143)( 53,142)( 54,144)( 55,113)( 56,112)
( 57,114)( 58,110)( 59,109)( 60,111)( 61,116)( 62,115)( 63,117)( 64,122)
( 65,121)( 66,123)( 67,119)( 68,118)( 69,120)( 70,125)( 71,124)( 72,126);;
s2 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)
( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 65, 66)( 68, 69)( 71, 72)
( 74, 75)( 77, 78)( 80, 81)( 83, 84)( 86, 87)( 89, 90)( 92, 93)( 95, 96)
( 98, 99)(101,102)(104,105)(107,108)(110,111)(113,114)(116,117)(119,120)
(122,123)(125,126)(128,129)(131,132)(134,135)(137,138)(140,141)(143,144);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(144)!(  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)
( 15, 17)( 19, 28)( 20, 30)( 21, 29)( 22, 34)( 23, 36)( 24, 35)( 25, 31)
( 26, 33)( 27, 32)( 37, 55)( 38, 57)( 39, 56)( 40, 61)( 41, 63)( 42, 62)
( 43, 58)( 44, 60)( 45, 59)( 46, 64)( 47, 66)( 48, 65)( 49, 70)( 50, 72)
( 51, 71)( 52, 67)( 53, 69)( 54, 68)( 73,109)( 74,111)( 75,110)( 76,115)
( 77,117)( 78,116)( 79,112)( 80,114)( 81,113)( 82,118)( 83,120)( 84,119)
( 85,124)( 86,126)( 87,125)( 88,121)( 89,123)( 90,122)( 91,136)( 92,138)
( 93,137)( 94,142)( 95,144)( 96,143)( 97,139)( 98,141)( 99,140)(100,127)
(101,129)(102,128)(103,133)(104,135)(105,134)(106,130)(107,132)(108,131);
s1 := Sym(144)!(  1, 77)(  2, 76)(  3, 78)(  4, 74)(  5, 73)(  6, 75)(  7, 80)
(  8, 79)(  9, 81)( 10, 86)( 11, 85)( 12, 87)( 13, 83)( 14, 82)( 15, 84)
( 16, 89)( 17, 88)( 18, 90)( 19,104)( 20,103)( 21,105)( 22,101)( 23,100)
( 24,102)( 25,107)( 26,106)( 27,108)( 28, 95)( 29, 94)( 30, 96)( 31, 92)
( 32, 91)( 33, 93)( 34, 98)( 35, 97)( 36, 99)( 37,131)( 38,130)( 39,132)
( 40,128)( 41,127)( 42,129)( 43,134)( 44,133)( 45,135)( 46,140)( 47,139)
( 48,141)( 49,137)( 50,136)( 51,138)( 52,143)( 53,142)( 54,144)( 55,113)
( 56,112)( 57,114)( 58,110)( 59,109)( 60,111)( 61,116)( 62,115)( 63,117)
( 64,122)( 65,121)( 66,123)( 67,119)( 68,118)( 69,120)( 70,125)( 71,124)
( 72,126);
s2 := Sym(144)!(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)
( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)
( 47, 48)( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 65, 66)( 68, 69)
( 71, 72)( 74, 75)( 77, 78)( 80, 81)( 83, 84)( 86, 87)( 89, 90)( 92, 93)
( 95, 96)( 98, 99)(101,102)(104,105)(107,108)(110,111)(113,114)(116,117)
(119,120)(122,123)(125,126)(128,129)(131,132)(134,135)(137,138)(140,141)
(143,144);
poly := sub<Sym(144)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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