Polytope of Type {12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*768j
if this polytope has a name.
Group : SmallGroup(768,1088556)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 64, 192, 32
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6}*384c
   4-fold quotients : {6,6}*192a
   8-fold quotients : {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   32-fold quotients : {3,3}*24
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope