Polytope of Type {8,12}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope