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Polytope of Type {6,64}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,64}*768
Also Known As : {6,64|2}. if this polytope has another name.
Group : SmallGroup(768,90609)
Rank : 3
Schlafli Type : {6,64}
Number of vertices, edges, etc : 6, 192, 64
Order of s0s1s2 : 192
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {6,32}*384
   3-fold quotients : {2,64}*256
   4-fold quotients : {6,16}*192
   6-fold quotients : {2,32}*128
   8-fold quotients : {6,8}*96
   12-fold quotients : {2,16}*64
   16-fold quotients : {6,4}*48a
   24-fold quotients : {2,8}*32
   32-fold quotients : {6,2}*24
   48-fold quotients : {2,4}*16
   64-fold quotients : {3,2}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 97)(  2, 99)(  3, 98)(  4,100)(  5,102)(  6,101)(  7,103)(  8,105)
(  9,104)( 10,106)( 11,108)( 12,107)( 13,109)( 14,111)( 15,110)( 16,112)
( 17,114)( 18,113)( 19,115)( 20,117)( 21,116)( 22,118)( 23,120)( 24,119)
( 25,121)( 26,123)( 27,122)( 28,124)( 29,126)( 30,125)( 31,127)( 32,129)
( 33,128)( 34,130)( 35,132)( 36,131)( 37,133)( 38,135)( 39,134)( 40,136)
( 41,138)( 42,137)( 43,139)( 44,141)( 45,140)( 46,142)( 47,144)( 48,143)
( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)( 56,153)
( 57,152)( 58,154)( 59,156)( 60,155)( 61,157)( 62,159)( 63,158)( 64,160)
( 65,162)( 66,161)( 67,163)( 68,165)( 69,164)( 70,166)( 71,168)( 72,167)
( 73,169)( 74,171)( 75,170)( 76,172)( 77,174)( 78,173)( 79,175)( 80,177)
( 81,176)( 82,178)( 83,180)( 84,179)( 85,181)( 86,183)( 87,182)( 88,184)
( 89,186)( 90,185)( 91,187)( 92,189)( 93,188)( 94,190)( 95,192)( 96,191)
(193,289)(194,291)(195,290)(196,292)(197,294)(198,293)(199,295)(200,297)
(201,296)(202,298)(203,300)(204,299)(205,301)(206,303)(207,302)(208,304)
(209,306)(210,305)(211,307)(212,309)(213,308)(214,310)(215,312)(216,311)
(217,313)(218,315)(219,314)(220,316)(221,318)(222,317)(223,319)(224,321)
(225,320)(226,322)(227,324)(228,323)(229,325)(230,327)(231,326)(232,328)
(233,330)(234,329)(235,331)(236,333)(237,332)(238,334)(239,336)(240,335)
(241,337)(242,339)(243,338)(244,340)(245,342)(246,341)(247,343)(248,345)
(249,344)(250,346)(251,348)(252,347)(253,349)(254,351)(255,350)(256,352)
(257,354)(258,353)(259,355)(260,357)(261,356)(262,358)(263,360)(264,359)
(265,361)(266,363)(267,362)(268,364)(269,366)(270,365)(271,367)(272,369)
(273,368)(274,370)(275,372)(276,371)(277,373)(278,375)(279,374)(280,376)
(281,378)(282,377)(283,379)(284,381)(285,380)(286,382)(287,384)(288,383);;
s1 := (  1, 99)(  2, 98)(  3, 97)(  4,102)(  5,101)(  6,100)(  7,108)(  8,107)
(  9,106)( 10,105)( 11,104)( 12,103)( 13,117)( 14,116)( 15,115)( 16,120)
( 17,119)( 18,118)( 19,111)( 20,110)( 21,109)( 22,114)( 23,113)( 24,112)
( 25,135)( 26,134)( 27,133)( 28,138)( 29,137)( 30,136)( 31,144)( 32,143)
( 33,142)( 34,141)( 35,140)( 36,139)( 37,123)( 38,122)( 39,121)( 40,126)
( 41,125)( 42,124)( 43,132)( 44,131)( 45,130)( 46,129)( 47,128)( 48,127)
( 49,171)( 50,170)( 51,169)( 52,174)( 53,173)( 54,172)( 55,180)( 56,179)
( 57,178)( 58,177)( 59,176)( 60,175)( 61,189)( 62,188)( 63,187)( 64,192)
( 65,191)( 66,190)( 67,183)( 68,182)( 69,181)( 70,186)( 71,185)( 72,184)
( 73,147)( 74,146)( 75,145)( 76,150)( 77,149)( 78,148)( 79,156)( 80,155)
( 81,154)( 82,153)( 83,152)( 84,151)( 85,165)( 86,164)( 87,163)( 88,168)
( 89,167)( 90,166)( 91,159)( 92,158)( 93,157)( 94,162)( 95,161)( 96,160)
(193,339)(194,338)(195,337)(196,342)(197,341)(198,340)(199,348)(200,347)
(201,346)(202,345)(203,344)(204,343)(205,357)(206,356)(207,355)(208,360)
(209,359)(210,358)(211,351)(212,350)(213,349)(214,354)(215,353)(216,352)
(217,375)(218,374)(219,373)(220,378)(221,377)(222,376)(223,384)(224,383)
(225,382)(226,381)(227,380)(228,379)(229,363)(230,362)(231,361)(232,366)
(233,365)(234,364)(235,372)(236,371)(237,370)(238,369)(239,368)(240,367)
(241,291)(242,290)(243,289)(244,294)(245,293)(246,292)(247,300)(248,299)
(249,298)(250,297)(251,296)(252,295)(253,309)(254,308)(255,307)(256,312)
(257,311)(258,310)(259,303)(260,302)(261,301)(262,306)(263,305)(264,304)
(265,327)(266,326)(267,325)(268,330)(269,329)(270,328)(271,336)(272,335)
(273,334)(274,333)(275,332)(276,331)(277,315)(278,314)(279,313)(280,318)
(281,317)(282,316)(283,324)(284,323)(285,322)(286,321)(287,320)(288,319);;
s2 := (  1,193)(  2,194)(  3,195)(  4,196)(  5,197)(  6,198)(  7,202)(  8,203)
(  9,204)( 10,199)( 11,200)( 12,201)( 13,211)( 14,212)( 15,213)( 16,214)
( 17,215)( 18,216)( 19,205)( 20,206)( 21,207)( 22,208)( 23,209)( 24,210)
( 25,229)( 26,230)( 27,231)( 28,232)( 29,233)( 30,234)( 31,238)( 32,239)
( 33,240)( 34,235)( 35,236)( 36,237)( 37,217)( 38,218)( 39,219)( 40,220)
( 41,221)( 42,222)( 43,226)( 44,227)( 45,228)( 46,223)( 47,224)( 48,225)
( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,274)( 56,275)
( 57,276)( 58,271)( 59,272)( 60,273)( 61,283)( 62,284)( 63,285)( 64,286)
( 65,287)( 66,288)( 67,277)( 68,278)( 69,279)( 70,280)( 71,281)( 72,282)
( 73,241)( 74,242)( 75,243)( 76,244)( 77,245)( 78,246)( 79,250)( 80,251)
( 81,252)( 82,247)( 83,248)( 84,249)( 85,259)( 86,260)( 87,261)( 88,262)
( 89,263)( 90,264)( 91,253)( 92,254)( 93,255)( 94,256)( 95,257)( 96,258)
( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)(104,299)
(105,300)(106,295)(107,296)(108,297)(109,307)(110,308)(111,309)(112,310)
(113,311)(114,312)(115,301)(116,302)(117,303)(118,304)(119,305)(120,306)
(121,325)(122,326)(123,327)(124,328)(125,329)(126,330)(127,334)(128,335)
(129,336)(130,331)(131,332)(132,333)(133,313)(134,314)(135,315)(136,316)
(137,317)(138,318)(139,322)(140,323)(141,324)(142,319)(143,320)(144,321)
(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,370)(152,371)
(153,372)(154,367)(155,368)(156,369)(157,379)(158,380)(159,381)(160,382)
(161,383)(162,384)(163,373)(164,374)(165,375)(166,376)(167,377)(168,378)
(169,337)(170,338)(171,339)(172,340)(173,341)(174,342)(175,346)(176,347)
(177,348)(178,343)(179,344)(180,345)(181,355)(182,356)(183,357)(184,358)
(185,359)(186,360)(187,349)(188,350)(189,351)(190,352)(191,353)(192,354);;
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*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(384)!(  1, 97)(  2, 99)(  3, 98)(  4,100)(  5,102)(  6,101)(  7,103)
(  8,105)(  9,104)( 10,106)( 11,108)( 12,107)( 13,109)( 14,111)( 15,110)
( 16,112)( 17,114)( 18,113)( 19,115)( 20,117)( 21,116)( 22,118)( 23,120)
( 24,119)( 25,121)( 26,123)( 27,122)( 28,124)( 29,126)( 30,125)( 31,127)
( 32,129)( 33,128)( 34,130)( 35,132)( 36,131)( 37,133)( 38,135)( 39,134)
( 40,136)( 41,138)( 42,137)( 43,139)( 44,141)( 45,140)( 46,142)( 47,144)
( 48,143)( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)
( 56,153)( 57,152)( 58,154)( 59,156)( 60,155)( 61,157)( 62,159)( 63,158)
( 64,160)( 65,162)( 66,161)( 67,163)( 68,165)( 69,164)( 70,166)( 71,168)
( 72,167)( 73,169)( 74,171)( 75,170)( 76,172)( 77,174)( 78,173)( 79,175)
( 80,177)( 81,176)( 82,178)( 83,180)( 84,179)( 85,181)( 86,183)( 87,182)
( 88,184)( 89,186)( 90,185)( 91,187)( 92,189)( 93,188)( 94,190)( 95,192)
( 96,191)(193,289)(194,291)(195,290)(196,292)(197,294)(198,293)(199,295)
(200,297)(201,296)(202,298)(203,300)(204,299)(205,301)(206,303)(207,302)
(208,304)(209,306)(210,305)(211,307)(212,309)(213,308)(214,310)(215,312)
(216,311)(217,313)(218,315)(219,314)(220,316)(221,318)(222,317)(223,319)
(224,321)(225,320)(226,322)(227,324)(228,323)(229,325)(230,327)(231,326)
(232,328)(233,330)(234,329)(235,331)(236,333)(237,332)(238,334)(239,336)
(240,335)(241,337)(242,339)(243,338)(244,340)(245,342)(246,341)(247,343)
(248,345)(249,344)(250,346)(251,348)(252,347)(253,349)(254,351)(255,350)
(256,352)(257,354)(258,353)(259,355)(260,357)(261,356)(262,358)(263,360)
(264,359)(265,361)(266,363)(267,362)(268,364)(269,366)(270,365)(271,367)
(272,369)(273,368)(274,370)(275,372)(276,371)(277,373)(278,375)(279,374)
(280,376)(281,378)(282,377)(283,379)(284,381)(285,380)(286,382)(287,384)
(288,383);
s1 := Sym(384)!(  1, 99)(  2, 98)(  3, 97)(  4,102)(  5,101)(  6,100)(  7,108)
(  8,107)(  9,106)( 10,105)( 11,104)( 12,103)( 13,117)( 14,116)( 15,115)
( 16,120)( 17,119)( 18,118)( 19,111)( 20,110)( 21,109)( 22,114)( 23,113)
( 24,112)( 25,135)( 26,134)( 27,133)( 28,138)( 29,137)( 30,136)( 31,144)
( 32,143)( 33,142)( 34,141)( 35,140)( 36,139)( 37,123)( 38,122)( 39,121)
( 40,126)( 41,125)( 42,124)( 43,132)( 44,131)( 45,130)( 46,129)( 47,128)
( 48,127)( 49,171)( 50,170)( 51,169)( 52,174)( 53,173)( 54,172)( 55,180)
( 56,179)( 57,178)( 58,177)( 59,176)( 60,175)( 61,189)( 62,188)( 63,187)
( 64,192)( 65,191)( 66,190)( 67,183)( 68,182)( 69,181)( 70,186)( 71,185)
( 72,184)( 73,147)( 74,146)( 75,145)( 76,150)( 77,149)( 78,148)( 79,156)
( 80,155)( 81,154)( 82,153)( 83,152)( 84,151)( 85,165)( 86,164)( 87,163)
( 88,168)( 89,167)( 90,166)( 91,159)( 92,158)( 93,157)( 94,162)( 95,161)
( 96,160)(193,339)(194,338)(195,337)(196,342)(197,341)(198,340)(199,348)
(200,347)(201,346)(202,345)(203,344)(204,343)(205,357)(206,356)(207,355)
(208,360)(209,359)(210,358)(211,351)(212,350)(213,349)(214,354)(215,353)
(216,352)(217,375)(218,374)(219,373)(220,378)(221,377)(222,376)(223,384)
(224,383)(225,382)(226,381)(227,380)(228,379)(229,363)(230,362)(231,361)
(232,366)(233,365)(234,364)(235,372)(236,371)(237,370)(238,369)(239,368)
(240,367)(241,291)(242,290)(243,289)(244,294)(245,293)(246,292)(247,300)
(248,299)(249,298)(250,297)(251,296)(252,295)(253,309)(254,308)(255,307)
(256,312)(257,311)(258,310)(259,303)(260,302)(261,301)(262,306)(263,305)
(264,304)(265,327)(266,326)(267,325)(268,330)(269,329)(270,328)(271,336)
(272,335)(273,334)(274,333)(275,332)(276,331)(277,315)(278,314)(279,313)
(280,318)(281,317)(282,316)(283,324)(284,323)(285,322)(286,321)(287,320)
(288,319);
s2 := Sym(384)!(  1,193)(  2,194)(  3,195)(  4,196)(  5,197)(  6,198)(  7,202)
(  8,203)(  9,204)( 10,199)( 11,200)( 12,201)( 13,211)( 14,212)( 15,213)
( 16,214)( 17,215)( 18,216)( 19,205)( 20,206)( 21,207)( 22,208)( 23,209)
( 24,210)( 25,229)( 26,230)( 27,231)( 28,232)( 29,233)( 30,234)( 31,238)
( 32,239)( 33,240)( 34,235)( 35,236)( 36,237)( 37,217)( 38,218)( 39,219)
( 40,220)( 41,221)( 42,222)( 43,226)( 44,227)( 45,228)( 46,223)( 47,224)
( 48,225)( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,274)
( 56,275)( 57,276)( 58,271)( 59,272)( 60,273)( 61,283)( 62,284)( 63,285)
( 64,286)( 65,287)( 66,288)( 67,277)( 68,278)( 69,279)( 70,280)( 71,281)
( 72,282)( 73,241)( 74,242)( 75,243)( 76,244)( 77,245)( 78,246)( 79,250)
( 80,251)( 81,252)( 82,247)( 83,248)( 84,249)( 85,259)( 86,260)( 87,261)
( 88,262)( 89,263)( 90,264)( 91,253)( 92,254)( 93,255)( 94,256)( 95,257)
( 96,258)( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)
(104,299)(105,300)(106,295)(107,296)(108,297)(109,307)(110,308)(111,309)
(112,310)(113,311)(114,312)(115,301)(116,302)(117,303)(118,304)(119,305)
(120,306)(121,325)(122,326)(123,327)(124,328)(125,329)(126,330)(127,334)
(128,335)(129,336)(130,331)(131,332)(132,333)(133,313)(134,314)(135,315)
(136,316)(137,317)(138,318)(139,322)(140,323)(141,324)(142,319)(143,320)
(144,321)(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,370)
(152,371)(153,372)(154,367)(155,368)(156,369)(157,379)(158,380)(159,381)
(160,382)(161,383)(162,384)(163,373)(164,374)(165,375)(166,376)(167,377)
(168,378)(169,337)(170,338)(171,339)(172,340)(173,341)(174,342)(175,346)
(176,347)(177,348)(178,343)(179,344)(180,345)(181,355)(182,356)(183,357)
(184,358)(185,359)(186,360)(187,349)(188,350)(189,351)(190,352)(191,353)
(192,354);
poly := sub<Sym(384)|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*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.
to this polytope