Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*768k
if this polytope has a name.
Group : SmallGroup(768,1086301)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 48, 192, 32
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 8
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 : {12,8}*384c, {12,8}*384d, {6,8}*384d
   4-fold quotients : {6,8}*192a
   8-fold quotients : {6,4}*96
   16-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,4}*24, {6,2}*24
   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 := (  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 := (  1,192)(  2,190)(  3,191)(  4,189)(  5,185)(  6,187)(  7,186)(  8,188)
(  9,175)( 10,173)( 11,176)( 12,174)( 13,170)( 14,172)( 15,169)( 16,171)
( 17,180)( 18,178)( 19,179)( 20,177)( 21,181)( 22,183)( 23,182)( 24,184)
( 25,165)( 26,167)( 27,166)( 28,168)( 29,164)( 30,162)( 31,163)( 32,161)
( 33,160)( 34,158)( 35,159)( 36,157)( 37,153)( 38,155)( 39,154)( 40,156)
( 41,143)( 42,141)( 43,144)( 44,142)( 45,138)( 46,140)( 47,137)( 48,139)
( 49,148)( 50,146)( 51,147)( 52,145)( 53,149)( 54,151)( 55,150)( 56,152)
( 57,133)( 58,135)( 59,134)( 60,136)( 61,132)( 62,130)( 63,131)( 64,129)
( 65,128)( 66,126)( 67,127)( 68,125)( 69,121)( 70,123)( 71,122)( 72,124)
( 73,111)( 74,109)( 75,112)( 76,110)( 77,106)( 78,108)( 79,105)( 80,107)
( 81,116)( 82,114)( 83,115)( 84,113)( 85,117)( 86,119)( 87,118)( 88,120)
( 89,101)( 90,103)( 91,102)( 92,104)( 93,100)( 94, 98)( 95, 99)( 96, 97)
(193,384)(194,382)(195,383)(196,381)(197,377)(198,379)(199,378)(200,380)
(201,367)(202,365)(203,368)(204,366)(205,362)(206,364)(207,361)(208,363)
(209,372)(210,370)(211,371)(212,369)(213,373)(214,375)(215,374)(216,376)
(217,357)(218,359)(219,358)(220,360)(221,356)(222,354)(223,355)(224,353)
(225,352)(226,350)(227,351)(228,349)(229,345)(230,347)(231,346)(232,348)
(233,335)(234,333)(235,336)(236,334)(237,330)(238,332)(239,329)(240,331)
(241,340)(242,338)(243,339)(244,337)(245,341)(246,343)(247,342)(248,344)
(249,325)(250,327)(251,326)(252,328)(253,324)(254,322)(255,323)(256,321)
(257,320)(258,318)(259,319)(260,317)(261,313)(262,315)(263,314)(264,316)
(265,303)(266,301)(267,304)(268,302)(269,298)(270,300)(271,297)(272,299)
(273,308)(274,306)(275,307)(276,305)(277,309)(278,311)(279,310)(280,312)
(281,293)(282,295)(283,294)(284,296)(285,292)(286,290)(287,291)(288,289);;
s2 := (  1,298)(  2,297)(  3,300)(  4,299)(  5,302)(  6,301)(  7,304)(  8,303)
(  9,296)( 10,295)( 11,294)( 12,293)( 13,292)( 14,291)( 15,290)( 16,289)
( 17,316)( 18,315)( 19,314)( 20,313)( 21,320)( 22,319)( 23,318)( 24,317)
( 25,310)( 26,309)( 27,312)( 28,311)( 29,306)( 30,305)( 31,308)( 32,307)
( 33,330)( 34,329)( 35,332)( 36,331)( 37,334)( 38,333)( 39,336)( 40,335)
( 41,328)( 42,327)( 43,326)( 44,325)( 45,324)( 46,323)( 47,322)( 48,321)
( 49,348)( 50,347)( 51,346)( 52,345)( 53,352)( 54,351)( 55,350)( 56,349)
( 57,342)( 58,341)( 59,344)( 60,343)( 61,338)( 62,337)( 63,340)( 64,339)
( 65,362)( 66,361)( 67,364)( 68,363)( 69,366)( 70,365)( 71,368)( 72,367)
( 73,360)( 74,359)( 75,358)( 76,357)( 77,356)( 78,355)( 79,354)( 80,353)
( 81,380)( 82,379)( 83,378)( 84,377)( 85,384)( 86,383)( 87,382)( 88,381)
( 89,374)( 90,373)( 91,376)( 92,375)( 93,370)( 94,369)( 95,372)( 96,371)
( 97,208)( 98,207)( 99,206)(100,205)(101,204)(102,203)(103,202)(104,201)
(105,194)(106,193)(107,196)(108,195)(109,198)(110,197)(111,200)(112,199)
(113,222)(114,221)(115,224)(116,223)(117,218)(118,217)(119,220)(120,219)
(121,212)(122,211)(123,210)(124,209)(125,216)(126,215)(127,214)(128,213)
(129,240)(130,239)(131,238)(132,237)(133,236)(134,235)(135,234)(136,233)
(137,226)(138,225)(139,228)(140,227)(141,230)(142,229)(143,232)(144,231)
(145,254)(146,253)(147,256)(148,255)(149,250)(150,249)(151,252)(152,251)
(153,244)(154,243)(155,242)(156,241)(157,248)(158,247)(159,246)(160,245)
(161,272)(162,271)(163,270)(164,269)(165,268)(166,267)(167,266)(168,265)
(169,258)(170,257)(171,260)(172,259)(173,262)(174,261)(175,264)(176,263)
(177,286)(178,285)(179,288)(180,287)(181,282)(182,281)(183,284)(184,283)
(185,276)(186,275)(187,274)(188,273)(189,280)(190,279)(191,278)(192,277);;
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*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*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)!(  1,192)(  2,190)(  3,191)(  4,189)(  5,185)(  6,187)(  7,186)
(  8,188)(  9,175)( 10,173)( 11,176)( 12,174)( 13,170)( 14,172)( 15,169)
( 16,171)( 17,180)( 18,178)( 19,179)( 20,177)( 21,181)( 22,183)( 23,182)
( 24,184)( 25,165)( 26,167)( 27,166)( 28,168)( 29,164)( 30,162)( 31,163)
( 32,161)( 33,160)( 34,158)( 35,159)( 36,157)( 37,153)( 38,155)( 39,154)
( 40,156)( 41,143)( 42,141)( 43,144)( 44,142)( 45,138)( 46,140)( 47,137)
( 48,139)( 49,148)( 50,146)( 51,147)( 52,145)( 53,149)( 54,151)( 55,150)
( 56,152)( 57,133)( 58,135)( 59,134)( 60,136)( 61,132)( 62,130)( 63,131)
( 64,129)( 65,128)( 66,126)( 67,127)( 68,125)( 69,121)( 70,123)( 71,122)
( 72,124)( 73,111)( 74,109)( 75,112)( 76,110)( 77,106)( 78,108)( 79,105)
( 80,107)( 81,116)( 82,114)( 83,115)( 84,113)( 85,117)( 86,119)( 87,118)
( 88,120)( 89,101)( 90,103)( 91,102)( 92,104)( 93,100)( 94, 98)( 95, 99)
( 96, 97)(193,384)(194,382)(195,383)(196,381)(197,377)(198,379)(199,378)
(200,380)(201,367)(202,365)(203,368)(204,366)(205,362)(206,364)(207,361)
(208,363)(209,372)(210,370)(211,371)(212,369)(213,373)(214,375)(215,374)
(216,376)(217,357)(218,359)(219,358)(220,360)(221,356)(222,354)(223,355)
(224,353)(225,352)(226,350)(227,351)(228,349)(229,345)(230,347)(231,346)
(232,348)(233,335)(234,333)(235,336)(236,334)(237,330)(238,332)(239,329)
(240,331)(241,340)(242,338)(243,339)(244,337)(245,341)(246,343)(247,342)
(248,344)(249,325)(250,327)(251,326)(252,328)(253,324)(254,322)(255,323)
(256,321)(257,320)(258,318)(259,319)(260,317)(261,313)(262,315)(263,314)
(264,316)(265,303)(266,301)(267,304)(268,302)(269,298)(270,300)(271,297)
(272,299)(273,308)(274,306)(275,307)(276,305)(277,309)(278,311)(279,310)
(280,312)(281,293)(282,295)(283,294)(284,296)(285,292)(286,290)(287,291)
(288,289);
s2 := Sym(384)!(  1,298)(  2,297)(  3,300)(  4,299)(  5,302)(  6,301)(  7,304)
(  8,303)(  9,296)( 10,295)( 11,294)( 12,293)( 13,292)( 14,291)( 15,290)
( 16,289)( 17,316)( 18,315)( 19,314)( 20,313)( 21,320)( 22,319)( 23,318)
( 24,317)( 25,310)( 26,309)( 27,312)( 28,311)( 29,306)( 30,305)( 31,308)
( 32,307)( 33,330)( 34,329)( 35,332)( 36,331)( 37,334)( 38,333)( 39,336)
( 40,335)( 41,328)( 42,327)( 43,326)( 44,325)( 45,324)( 46,323)( 47,322)
( 48,321)( 49,348)( 50,347)( 51,346)( 52,345)( 53,352)( 54,351)( 55,350)
( 56,349)( 57,342)( 58,341)( 59,344)( 60,343)( 61,338)( 62,337)( 63,340)
( 64,339)( 65,362)( 66,361)( 67,364)( 68,363)( 69,366)( 70,365)( 71,368)
( 72,367)( 73,360)( 74,359)( 75,358)( 76,357)( 77,356)( 78,355)( 79,354)
( 80,353)( 81,380)( 82,379)( 83,378)( 84,377)( 85,384)( 86,383)( 87,382)
( 88,381)( 89,374)( 90,373)( 91,376)( 92,375)( 93,370)( 94,369)( 95,372)
( 96,371)( 97,208)( 98,207)( 99,206)(100,205)(101,204)(102,203)(103,202)
(104,201)(105,194)(106,193)(107,196)(108,195)(109,198)(110,197)(111,200)
(112,199)(113,222)(114,221)(115,224)(116,223)(117,218)(118,217)(119,220)
(120,219)(121,212)(122,211)(123,210)(124,209)(125,216)(126,215)(127,214)
(128,213)(129,240)(130,239)(131,238)(132,237)(133,236)(134,235)(135,234)
(136,233)(137,226)(138,225)(139,228)(140,227)(141,230)(142,229)(143,232)
(144,231)(145,254)(146,253)(147,256)(148,255)(149,250)(150,249)(151,252)
(152,251)(153,244)(154,243)(155,242)(156,241)(157,248)(158,247)(159,246)
(160,245)(161,272)(162,271)(163,270)(164,269)(165,268)(166,267)(167,266)
(168,265)(169,258)(170,257)(171,260)(172,259)(173,262)(174,261)(175,264)
(176,263)(177,286)(178,285)(179,288)(180,287)(181,282)(182,281)(183,284)
(184,283)(185,276)(186,275)(187,274)(188,273)(189,280)(190,279)(191,278)
(192,277);
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*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1 >;

References : None.
to this polytope