Polytope of Type {6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*768c
if this polytope has a name.
Group : SmallGroup(768,1086301)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 32, 192, 64
Order of s₀s₁s₂ : 8
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 : {3,12}*384, {6,6}*384e
   4-fold quotients : {3,6}*192, {6,12}*192b
   8-fold quotients : {3,12}*96, {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 := (  3,  4)(  5,  6)(  9, 15)( 10, 16)( 11, 14)( 12, 13)( 17, 28)( 18, 27)
( 19, 25)( 20, 26)( 21, 31)( 22, 32)( 23, 30)( 24, 29)( 33, 65)( 34, 66)
( 35, 68)( 36, 67)( 37, 70)( 38, 69)( 39, 71)( 40, 72)( 41, 79)( 42, 80)
( 43, 78)( 44, 77)( 45, 76)( 46, 75)( 47, 73)( 48, 74)( 49, 92)( 50, 91)
( 51, 89)( 52, 90)( 53, 95)( 54, 96)( 55, 94)( 56, 93)( 57, 83)( 58, 84)
( 59, 82)( 60, 81)( 61, 88)( 62, 87)( 63, 85)( 64, 86)( 97,103)( 98,104)
( 99,102)(100,101)(107,108)(109,110)(113,126)(114,125)(115,127)(116,128)
(117,121)(118,122)(119,124)(120,123)(129,167)(130,168)(131,166)(132,165)
(133,164)(134,163)(135,161)(136,162)(137,169)(138,170)(139,172)(140,171)
(141,174)(142,173)(143,175)(144,176)(145,190)(146,189)(147,191)(148,192)
(149,185)(150,186)(151,188)(152,187)(153,181)(154,182)(155,184)(156,183)
(157,178)(158,177)(159,179)(160,180)(195,196)(197,198)(201,207)(202,208)
(203,206)(204,205)(209,220)(210,219)(211,217)(212,218)(213,223)(214,224)
(215,222)(216,221)(225,257)(226,258)(227,260)(228,259)(229,262)(230,261)
(231,263)(232,264)(233,271)(234,272)(235,270)(236,269)(237,268)(238,267)
(239,265)(240,266)(241,284)(242,283)(243,281)(244,282)(245,287)(246,288)
(247,286)(248,285)(249,275)(250,276)(251,274)(252,273)(253,280)(254,279)
(255,277)(256,278)(289,295)(290,296)(291,294)(292,293)(299,300)(301,302)
(305,318)(306,317)(307,319)(308,320)(309,313)(310,314)(311,316)(312,315)
(321,359)(322,360)(323,358)(324,357)(325,356)(326,355)(327,353)(328,354)
(329,361)(330,362)(331,364)(332,363)(333,366)(334,365)(335,367)(336,368)
(337,382)(338,381)(339,383)(340,384)(341,377)(342,378)(343,380)(344,379)
(345,373)(346,374)(347,376)(348,375)(349,370)(350,369)(351,371)(352,372);;
s1 := (  1,257)(  2,259)(  3,258)(  4,260)(  5,264)(  6,262)(  7,263)(  8,261)
(  9,280)( 10,278)( 11,279)( 12,277)( 13,273)( 14,275)( 15,274)( 16,276)
( 17,269)( 18,271)( 19,270)( 20,272)( 21,268)( 22,266)( 23,267)( 24,265)
( 25,286)( 26,288)( 27,285)( 28,287)( 29,283)( 30,281)( 31,284)( 32,282)
( 33,225)( 34,227)( 35,226)( 36,228)( 37,232)( 38,230)( 39,231)( 40,229)
( 41,248)( 42,246)( 43,247)( 44,245)( 45,241)( 46,243)( 47,242)( 48,244)
( 49,237)( 50,239)( 51,238)( 52,240)( 53,236)( 54,234)( 55,235)( 56,233)
( 57,254)( 58,256)( 59,253)( 60,255)( 61,251)( 62,249)( 63,252)( 64,250)
( 65,193)( 66,195)( 67,194)( 68,196)( 69,200)( 70,198)( 71,199)( 72,197)
( 73,216)( 74,214)( 75,215)( 76,213)( 77,209)( 78,211)( 79,210)( 80,212)
( 81,205)( 82,207)( 83,206)( 84,208)( 85,204)( 86,202)( 87,203)( 88,201)
( 89,222)( 90,224)( 91,221)( 92,223)( 93,219)( 94,217)( 95,220)( 96,218)
( 97,359)( 98,357)( 99,360)(100,358)(101,354)(102,356)(103,353)(104,355)
(105,370)(106,372)(107,369)(108,371)(109,375)(110,373)(111,376)(112,374)
(113,363)(114,361)(115,364)(116,362)(117,366)(118,368)(119,365)(120,367)
(121,380)(122,378)(123,379)(124,377)(125,381)(126,383)(127,382)(128,384)
(129,327)(130,325)(131,328)(132,326)(133,322)(134,324)(135,321)(136,323)
(137,338)(138,340)(139,337)(140,339)(141,343)(142,341)(143,344)(144,342)
(145,331)(146,329)(147,332)(148,330)(149,334)(150,336)(151,333)(152,335)
(153,348)(154,346)(155,347)(156,345)(157,349)(158,351)(159,350)(160,352)
(161,295)(162,293)(163,296)(164,294)(165,290)(166,292)(167,289)(168,291)
(169,306)(170,308)(171,305)(172,307)(173,311)(174,309)(175,312)(176,310)
(177,299)(178,297)(179,300)(180,298)(181,302)(182,304)(183,301)(184,303)
(185,316)(186,314)(187,315)(188,313)(189,317)(190,319)(191,318)(192,320);;
s2 := (  1,106)(  2,105)(  3,107)(  4,108)(  5,109)(  6,110)(  7,112)(  8,111)
(  9, 98)( 10, 97)( 11, 99)( 12,100)( 13,101)( 14,102)( 15,104)( 16,103)
( 17,119)( 18,120)( 19,118)( 20,117)( 21,116)( 22,115)( 23,113)( 24,114)
( 25,122)( 26,121)( 27,123)( 28,124)( 29,125)( 30,126)( 31,128)( 32,127)
( 33,170)( 34,169)( 35,171)( 36,172)( 37,173)( 38,174)( 39,176)( 40,175)
( 41,162)( 42,161)( 43,163)( 44,164)( 45,165)( 46,166)( 47,168)( 48,167)
( 49,183)( 50,184)( 51,182)( 52,181)( 53,180)( 54,179)( 55,177)( 56,178)
( 57,186)( 58,185)( 59,187)( 60,188)( 61,189)( 62,190)( 63,192)( 64,191)
( 65,138)( 66,137)( 67,139)( 68,140)( 69,141)( 70,142)( 71,144)( 72,143)
( 73,130)( 74,129)( 75,131)( 76,132)( 77,133)( 78,134)( 79,136)( 80,135)
( 81,151)( 82,152)( 83,150)( 84,149)( 85,148)( 86,147)( 87,145)( 88,146)
( 89,154)( 90,153)( 91,155)( 92,156)( 93,157)( 94,158)( 95,160)( 96,159)
(193,298)(194,297)(195,299)(196,300)(197,301)(198,302)(199,304)(200,303)
(201,290)(202,289)(203,291)(204,292)(205,293)(206,294)(207,296)(208,295)
(209,311)(210,312)(211,310)(212,309)(213,308)(214,307)(215,305)(216,306)
(217,314)(218,313)(219,315)(220,316)(221,317)(222,318)(223,320)(224,319)
(225,362)(226,361)(227,363)(228,364)(229,365)(230,366)(231,368)(232,367)
(233,354)(234,353)(235,355)(236,356)(237,357)(238,358)(239,360)(240,359)
(241,375)(242,376)(243,374)(244,373)(245,372)(246,371)(247,369)(248,370)
(249,378)(250,377)(251,379)(252,380)(253,381)(254,382)(255,384)(256,383)
(257,330)(258,329)(259,331)(260,332)(261,333)(262,334)(263,336)(264,335)
(265,322)(266,321)(267,323)(268,324)(269,325)(270,326)(271,328)(272,327)
(273,343)(274,344)(275,342)(276,341)(277,340)(278,339)(279,337)(280,338)
(281,346)(282,345)(283,347)(284,348)(285,349)(286,350)(287,352)(288,351);;
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, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope