Polytope of Type {64,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {64,6}*768
Also Known As : {64,6|2}. if this polytope has another name.
Group : SmallGroup(768,90609)
Rank : 3
Schlafli Type : {64,6}
Number of vertices, edges, etc : 64, 192, 6
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 : {32,6}*384
   3-fold quotients : {64,2}*256
   4-fold quotients : {16,6}*192
   6-fold quotients : {32,2}*128
   8-fold quotients : {8,6}*96
   12-fold quotients : {16,2}*64
   16-fold quotients : {4,6}*48a
   24-fold quotients : {8,2}*32
   32-fold quotients : {2,6}*24
   48-fold quotients : {4,2}*16
   64-fold quotients : {2,3}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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