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Polytope of Type {6,32}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,32}*384
Also Known As : {6,32|2}. if this polytope has another name.
Group : SmallGroup(384,1951)
Rank : 3
Schlafli Type : {6,32}
Number of vertices, edges, etc : 6, 96, 32
Order of s0s1s2 : 96
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,32,2} of size 768
Vertex Figure Of :
   {2,6,32} of size 768
   {3,6,32} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,16}*192
   3-fold quotients : {2,32}*128
   4-fold quotients : {6,8}*96
   6-fold quotients : {2,16}*64
   8-fold quotients : {6,4}*48a
   12-fold quotients : {2,8}*32
   16-fold quotients : {6,2}*24
   24-fold quotients : {2,4}*16
   32-fold quotients : {3,2}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,32}*768a, {6,64}*768
   3-fold covers : {18,32}*1152, {6,96}*1152a, {6,96}*1152c
   5-fold covers : {30,32}*1920, {6,160}*1920
Permutation Representation (GAP) :
s0 := (  1, 49)(  2, 51)(  3, 50)(  4, 52)(  5, 54)(  6, 53)(  7, 55)(  8, 57)
(  9, 56)( 10, 58)( 11, 60)( 12, 59)( 13, 61)( 14, 63)( 15, 62)( 16, 64)
( 17, 66)( 18, 65)( 19, 67)( 20, 69)( 21, 68)( 22, 70)( 23, 72)( 24, 71)
( 25, 73)( 26, 75)( 27, 74)( 28, 76)( 29, 78)( 30, 77)( 31, 79)( 32, 81)
( 33, 80)( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 87)( 39, 86)( 40, 88)
( 41, 90)( 42, 89)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 96)( 48, 95)
( 97,145)( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,151)(104,153)
(105,152)(106,154)(107,156)(108,155)(109,157)(110,159)(111,158)(112,160)
(113,162)(114,161)(115,163)(116,165)(117,164)(118,166)(119,168)(120,167)
(121,169)(122,171)(123,170)(124,172)(125,174)(126,173)(127,175)(128,177)
(129,176)(130,178)(131,180)(132,179)(133,181)(134,183)(135,182)(136,184)
(137,186)(138,185)(139,187)(140,189)(141,188)(142,190)(143,192)(144,191);;
s1 := (  1, 50)(  2, 49)(  3, 51)(  4, 53)(  5, 52)(  6, 54)(  7, 59)(  8, 58)
(  9, 60)( 10, 56)( 11, 55)( 12, 57)( 13, 68)( 14, 67)( 15, 69)( 16, 71)
( 17, 70)( 18, 72)( 19, 62)( 20, 61)( 21, 63)( 22, 65)( 23, 64)( 24, 66)
( 25, 86)( 26, 85)( 27, 87)( 28, 89)( 29, 88)( 30, 90)( 31, 95)( 32, 94)
( 33, 96)( 34, 92)( 35, 91)( 36, 93)( 37, 74)( 38, 73)( 39, 75)( 40, 77)
( 41, 76)( 42, 78)( 43, 83)( 44, 82)( 45, 84)( 46, 80)( 47, 79)( 48, 81)
( 97,170)( 98,169)( 99,171)(100,173)(101,172)(102,174)(103,179)(104,178)
(105,180)(106,176)(107,175)(108,177)(109,188)(110,187)(111,189)(112,191)
(113,190)(114,192)(115,182)(116,181)(117,183)(118,185)(119,184)(120,186)
(121,146)(122,145)(123,147)(124,149)(125,148)(126,150)(127,155)(128,154)
(129,156)(130,152)(131,151)(132,153)(133,164)(134,163)(135,165)(136,167)
(137,166)(138,168)(139,158)(140,157)(141,159)(142,161)(143,160)(144,162);;
s2 := (  1, 97)(  2, 98)(  3, 99)(  4,100)(  5,101)(  6,102)(  7,106)(  8,107)
(  9,108)( 10,103)( 11,104)( 12,105)( 13,115)( 14,116)( 15,117)( 16,118)
( 17,119)( 18,120)( 19,109)( 20,110)( 21,111)( 22,112)( 23,113)( 24,114)
( 25,133)( 26,134)( 27,135)( 28,136)( 29,137)( 30,138)( 31,142)( 32,143)
( 33,144)( 34,139)( 35,140)( 36,141)( 37,121)( 38,122)( 39,123)( 40,124)
( 41,125)( 42,126)( 43,130)( 44,131)( 45,132)( 46,127)( 47,128)( 48,129)
( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,154)( 56,155)
( 57,156)( 58,151)( 59,152)( 60,153)( 61,163)( 62,164)( 63,165)( 64,166)
( 65,167)( 66,168)( 67,157)( 68,158)( 69,159)( 70,160)( 71,161)( 72,162)
( 73,181)( 74,182)( 75,183)( 76,184)( 77,185)( 78,186)( 79,190)( 80,191)
( 81,192)( 82,187)( 83,188)( 84,189)( 85,169)( 86,170)( 87,171)( 88,172)
( 89,173)( 90,174)( 91,178)( 92,179)( 93,180)( 94,175)( 95,176)( 96,177);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(192)!(  1, 49)(  2, 51)(  3, 50)(  4, 52)(  5, 54)(  6, 53)(  7, 55)
(  8, 57)(  9, 56)( 10, 58)( 11, 60)( 12, 59)( 13, 61)( 14, 63)( 15, 62)
( 16, 64)( 17, 66)( 18, 65)( 19, 67)( 20, 69)( 21, 68)( 22, 70)( 23, 72)
( 24, 71)( 25, 73)( 26, 75)( 27, 74)( 28, 76)( 29, 78)( 30, 77)( 31, 79)
( 32, 81)( 33, 80)( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 87)( 39, 86)
( 40, 88)( 41, 90)( 42, 89)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 96)
( 48, 95)( 97,145)( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,151)
(104,153)(105,152)(106,154)(107,156)(108,155)(109,157)(110,159)(111,158)
(112,160)(113,162)(114,161)(115,163)(116,165)(117,164)(118,166)(119,168)
(120,167)(121,169)(122,171)(123,170)(124,172)(125,174)(126,173)(127,175)
(128,177)(129,176)(130,178)(131,180)(132,179)(133,181)(134,183)(135,182)
(136,184)(137,186)(138,185)(139,187)(140,189)(141,188)(142,190)(143,192)
(144,191);
s1 := Sym(192)!(  1, 50)(  2, 49)(  3, 51)(  4, 53)(  5, 52)(  6, 54)(  7, 59)
(  8, 58)(  9, 60)( 10, 56)( 11, 55)( 12, 57)( 13, 68)( 14, 67)( 15, 69)
( 16, 71)( 17, 70)( 18, 72)( 19, 62)( 20, 61)( 21, 63)( 22, 65)( 23, 64)
( 24, 66)( 25, 86)( 26, 85)( 27, 87)( 28, 89)( 29, 88)( 30, 90)( 31, 95)
( 32, 94)( 33, 96)( 34, 92)( 35, 91)( 36, 93)( 37, 74)( 38, 73)( 39, 75)
( 40, 77)( 41, 76)( 42, 78)( 43, 83)( 44, 82)( 45, 84)( 46, 80)( 47, 79)
( 48, 81)( 97,170)( 98,169)( 99,171)(100,173)(101,172)(102,174)(103,179)
(104,178)(105,180)(106,176)(107,175)(108,177)(109,188)(110,187)(111,189)
(112,191)(113,190)(114,192)(115,182)(116,181)(117,183)(118,185)(119,184)
(120,186)(121,146)(122,145)(123,147)(124,149)(125,148)(126,150)(127,155)
(128,154)(129,156)(130,152)(131,151)(132,153)(133,164)(134,163)(135,165)
(136,167)(137,166)(138,168)(139,158)(140,157)(141,159)(142,161)(143,160)
(144,162);
s2 := Sym(192)!(  1, 97)(  2, 98)(  3, 99)(  4,100)(  5,101)(  6,102)(  7,106)
(  8,107)(  9,108)( 10,103)( 11,104)( 12,105)( 13,115)( 14,116)( 15,117)
( 16,118)( 17,119)( 18,120)( 19,109)( 20,110)( 21,111)( 22,112)( 23,113)
( 24,114)( 25,133)( 26,134)( 27,135)( 28,136)( 29,137)( 30,138)( 31,142)
( 32,143)( 33,144)( 34,139)( 35,140)( 36,141)( 37,121)( 38,122)( 39,123)
( 40,124)( 41,125)( 42,126)( 43,130)( 44,131)( 45,132)( 46,127)( 47,128)
( 48,129)( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,154)
( 56,155)( 57,156)( 58,151)( 59,152)( 60,153)( 61,163)( 62,164)( 63,165)
( 64,166)( 65,167)( 66,168)( 67,157)( 68,158)( 69,159)( 70,160)( 71,161)
( 72,162)( 73,181)( 74,182)( 75,183)( 76,184)( 77,185)( 78,186)( 79,190)
( 80,191)( 81,192)( 82,187)( 83,188)( 84,189)( 85,169)( 86,170)( 87,171)
( 88,172)( 89,173)( 90,174)( 91,178)( 92,179)( 93,180)( 94,175)( 95,176)
( 96,177);
poly := sub<Sym(192)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
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