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Polytope of Type {6,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,48}*576c
if this polytope has a name.
Group : SmallGroup(576,2907)
Rank : 3
Schlafli Type : {6,48}
Number of vertices, edges, etc : 6, 144, 48
Order of s0s1s2 : 48
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,48,2} of size 1152
Vertex Figure Of :
   {2,6,48} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,24}*288c
   3-fold quotients : {6,16}*192
   4-fold quotients : {6,12}*144c
   6-fold quotients : {6,8}*96
   8-fold quotients : {6,6}*72c
   9-fold quotients : {2,16}*64
   12-fold quotients : {6,4}*48a
   16-fold quotients : {3,6}*36
   18-fold quotients : {2,8}*32
   24-fold quotients : {6,2}*24
   36-fold quotients : {2,4}*16
   48-fold quotients : {3,2}*12
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,48}*1152c, {6,96}*1152a
   3-fold covers : {18,48}*1728b, {6,48}*1728c, {6,48}*1728f
Permutation Representation (GAP) :
s0 := (  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)
( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)( 51, 53)
( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 65, 66)( 67, 70)( 68, 72)( 69, 71)
( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)( 85, 88)( 86, 90)( 87, 89)
( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)
(110,111)(112,115)(113,117)(114,116)(119,120)(121,124)(122,126)(123,125)
(128,129)(130,133)(131,135)(132,134)(137,138)(139,142)(140,144)(141,143);;
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)( 19, 28)( 20, 30)
( 21, 29)( 22, 31)( 23, 33)( 24, 32)( 25, 34)( 26, 36)( 27, 35)( 37, 55)
( 38, 57)( 39, 56)( 40, 58)( 41, 60)( 42, 59)( 43, 61)( 44, 63)( 45, 62)
( 46, 64)( 47, 66)( 48, 65)( 49, 67)( 50, 69)( 51, 68)( 52, 70)( 53, 72)
( 54, 71)( 73,109)( 74,111)( 75,110)( 76,112)( 77,114)( 78,113)( 79,115)
( 80,117)( 81,116)( 82,118)( 83,120)( 84,119)( 85,121)( 86,123)( 87,122)
( 88,124)( 89,126)( 90,125)( 91,136)( 92,138)( 93,137)( 94,139)( 95,141)
( 96,140)( 97,142)( 98,144)( 99,143)(100,127)(101,129)(102,128)(103,130)
(104,132)(105,131)(106,133)(107,135)(108,134);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*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*s0*s1*s2*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)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)
( 51, 53)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 65, 66)( 67, 70)( 68, 72)
( 69, 71)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)( 85, 88)( 86, 90)
( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)
(105,107)(110,111)(112,115)(113,117)(114,116)(119,120)(121,124)(122,126)
(123,125)(128,129)(130,133)(131,135)(132,134)(137,138)(139,142)(140,144)
(141,143);
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)( 19, 28)
( 20, 30)( 21, 29)( 22, 31)( 23, 33)( 24, 32)( 25, 34)( 26, 36)( 27, 35)
( 37, 55)( 38, 57)( 39, 56)( 40, 58)( 41, 60)( 42, 59)( 43, 61)( 44, 63)
( 45, 62)( 46, 64)( 47, 66)( 48, 65)( 49, 67)( 50, 69)( 51, 68)( 52, 70)
( 53, 72)( 54, 71)( 73,109)( 74,111)( 75,110)( 76,112)( 77,114)( 78,113)
( 79,115)( 80,117)( 81,116)( 82,118)( 83,120)( 84,119)( 85,121)( 86,123)
( 87,122)( 88,124)( 89,126)( 90,125)( 91,136)( 92,138)( 93,137)( 94,139)
( 95,141)( 96,140)( 97,142)( 98,144)( 99,143)(100,127)(101,129)(102,128)
(103,130)(104,132)(105,131)(106,133)(107,135)(108,134);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*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*s0*s1*s2*s1 >; 
 
References : None.
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