Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*768h
if this polytope has a name.
Group : SmallGroup(768,1086012)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 48, 192, 32
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
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 : {12,4}*384c, {6,8}*384c
   4-fold quotients : {6,4}*192a
   8-fold quotients : {12,4}*96c
   16-fold quotients : {6,4}*48c
   32-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope