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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}*576a
Also Known As : {48,6|2}. if this polytope has another 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 : 2
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}*288a
   3-fold quotients : {48,2}*192, {16,6}*192
   4-fold quotients : {12,6}*144a
   6-fold quotients : {24,2}*96, {8,6}*96
   8-fold quotients : {6,6}*72a
   9-fold quotients : {16,2}*64
   12-fold quotients : {12,2}*48, {4,6}*48a
   18-fold quotients : {8,2}*32
   24-fold quotients : {2,6}*24, {6,2}*24
   36-fold quotients : {4,2}*16
   48-fold quotients : {2,3}*12, {3,2}*12
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {48,12}*1152b, {96,6}*1152c
   3-fold covers : {144,6}*1728a, {48,18}*1728a, {48,6}*1728b, {48,6}*1728f
Permutation Representation (GAP) :
s0 := (  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 19, 28)( 20, 29)
( 21, 30)( 22, 34)( 23, 35)( 24, 36)( 25, 31)( 26, 32)( 27, 33)( 37, 55)
( 38, 56)( 39, 57)( 40, 61)( 41, 62)( 42, 63)( 43, 58)( 44, 59)( 45, 60)
( 46, 64)( 47, 65)( 48, 66)( 49, 70)( 50, 71)( 51, 72)( 52, 67)( 53, 68)
( 54, 69)( 73,109)( 74,110)( 75,111)( 76,115)( 77,116)( 78,117)( 79,112)
( 80,113)( 81,114)( 82,118)( 83,119)( 84,120)( 85,124)( 86,125)( 87,126)
( 88,121)( 89,122)( 90,123)( 91,136)( 92,137)( 93,138)( 94,142)( 95,143)
( 96,144)( 97,139)( 98,140)( 99,141)(100,127)(101,128)(102,129)(103,133)
(104,134)(105,135)(106,130)(107,131)(108,132);;
s1 := (  1, 76)(  2, 78)(  3, 77)(  4, 73)(  5, 75)(  6, 74)(  7, 79)(  8, 81)
(  9, 80)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)( 16, 88)
( 17, 90)( 18, 89)( 19,103)( 20,105)( 21,104)( 22,100)( 23,102)( 24,101)
( 25,106)( 26,108)( 27,107)( 28, 94)( 29, 96)( 30, 95)( 31, 91)( 32, 93)
( 33, 92)( 34, 97)( 35, 99)( 36, 98)( 37,130)( 38,132)( 39,131)( 40,127)
( 41,129)( 42,128)( 43,133)( 44,135)( 45,134)( 46,139)( 47,141)( 48,140)
( 49,136)( 50,138)( 51,137)( 52,142)( 53,144)( 54,143)( 55,112)( 56,114)
( 57,113)( 58,109)( 59,111)( 60,110)( 61,115)( 62,117)( 63,116)( 64,121)
( 65,123)( 66,122)( 67,118)( 68,120)( 69,119)( 70,124)( 71,126)( 72,125);;
s2 := (  1,  2)(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)
( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)
( 73, 74)( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)( 94, 95)
( 97, 98)(100,101)(103,104)(106,107)(109,110)(112,113)(115,116)(118,119)
(121,122)(124,125)(127,128)(130,131)(133,134)(136,137)(139,140)(142,143);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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)!(  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 19, 28)
( 20, 29)( 21, 30)( 22, 34)( 23, 35)( 24, 36)( 25, 31)( 26, 32)( 27, 33)
( 37, 55)( 38, 56)( 39, 57)( 40, 61)( 41, 62)( 42, 63)( 43, 58)( 44, 59)
( 45, 60)( 46, 64)( 47, 65)( 48, 66)( 49, 70)( 50, 71)( 51, 72)( 52, 67)
( 53, 68)( 54, 69)( 73,109)( 74,110)( 75,111)( 76,115)( 77,116)( 78,117)
( 79,112)( 80,113)( 81,114)( 82,118)( 83,119)( 84,120)( 85,124)( 86,125)
( 87,126)( 88,121)( 89,122)( 90,123)( 91,136)( 92,137)( 93,138)( 94,142)
( 95,143)( 96,144)( 97,139)( 98,140)( 99,141)(100,127)(101,128)(102,129)
(103,133)(104,134)(105,135)(106,130)(107,131)(108,132);
s1 := Sym(144)!(  1, 76)(  2, 78)(  3, 77)(  4, 73)(  5, 75)(  6, 74)(  7, 79)
(  8, 81)(  9, 80)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)
( 16, 88)( 17, 90)( 18, 89)( 19,103)( 20,105)( 21,104)( 22,100)( 23,102)
( 24,101)( 25,106)( 26,108)( 27,107)( 28, 94)( 29, 96)( 30, 95)( 31, 91)
( 32, 93)( 33, 92)( 34, 97)( 35, 99)( 36, 98)( 37,130)( 38,132)( 39,131)
( 40,127)( 41,129)( 42,128)( 43,133)( 44,135)( 45,134)( 46,139)( 47,141)
( 48,140)( 49,136)( 50,138)( 51,137)( 52,142)( 53,144)( 54,143)( 55,112)
( 56,114)( 57,113)( 58,109)( 59,111)( 60,110)( 61,115)( 62,117)( 63,116)
( 64,121)( 65,123)( 66,122)( 67,118)( 68,120)( 69,119)( 70,124)( 71,126)
( 72,125);
s2 := Sym(144)!(  1,  2)(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)
( 22, 23)( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)
( 46, 47)( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)
( 70, 71)( 73, 74)( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)
( 94, 95)( 97, 98)(100,101)(103,104)(106,107)(109,110)(112,113)(115,116)
(118,119)(121,122)(124,125)(127,128)(130,131)(133,134)(136,137)(139,140)
(142,143);
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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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