Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*768c
if this polytope has a name.
Group : SmallGroup(768,90301)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 48, 192, 32
Order of s₀s₁s₂ : 24
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 : {12,4}*384a
   3-fold quotients : {4,8}*256c
   4-fold quotients : {12,4}*192a
   6-fold quotients : {4,4}*128
   8-fold quotients : {12,4}*96a
   12-fold quotients : {4,4}*64
   16-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {4,4}*32
   32-fold quotients : {6,2}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   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 := (  1, 97)(  2, 99)(  3, 98)(  4,100)(  5,102)(  6,101)(  7,106)(  8,108)
(  9,107)( 10,103)( 11,105)( 12,104)( 13,112)( 14,114)( 15,113)( 16,109)
( 17,111)( 18,110)( 19,115)( 20,117)( 21,116)( 22,118)( 23,120)( 24,119)
( 25,121)( 26,123)( 27,122)( 28,124)( 29,126)( 30,125)( 31,130)( 32,132)
( 33,131)( 34,127)( 35,129)( 36,128)( 37,136)( 38,138)( 39,137)( 40,133)
( 41,135)( 42,134)( 43,139)( 44,141)( 45,140)( 46,142)( 47,144)( 48,143)
( 49,157)( 50,159)( 51,158)( 52,160)( 53,162)( 54,161)( 55,166)( 56,168)
( 57,167)( 58,163)( 59,165)( 60,164)( 61,145)( 62,147)( 63,146)( 64,148)
( 65,150)( 66,149)( 67,154)( 68,156)( 69,155)( 70,151)( 71,153)( 72,152)
( 73,184)( 74,186)( 75,185)( 76,181)( 77,183)( 78,182)( 79,187)( 80,189)
( 81,188)( 82,190)( 83,192)( 84,191)( 85,172)( 86,174)( 87,173)( 88,169)
( 89,171)( 90,170)( 91,175)( 92,177)( 93,176)( 94,178)( 95,180)( 96,179)
(193,289)(194,291)(195,290)(196,292)(197,294)(198,293)(199,298)(200,300)
(201,299)(202,295)(203,297)(204,296)(205,304)(206,306)(207,305)(208,301)
(209,303)(210,302)(211,307)(212,309)(213,308)(214,310)(215,312)(216,311)
(217,313)(218,315)(219,314)(220,316)(221,318)(222,317)(223,322)(224,324)
(225,323)(226,319)(227,321)(228,320)(229,328)(230,330)(231,329)(232,325)
(233,327)(234,326)(235,331)(236,333)(237,332)(238,334)(239,336)(240,335)
(241,349)(242,351)(243,350)(244,352)(245,354)(246,353)(247,358)(248,360)
(249,359)(250,355)(251,357)(252,356)(253,337)(254,339)(255,338)(256,340)
(257,342)(258,341)(259,346)(260,348)(261,347)(262,343)(263,345)(264,344)
(265,376)(266,378)(267,377)(268,373)(269,375)(270,374)(271,379)(272,381)
(273,380)(274,382)(275,384)(276,383)(277,364)(278,366)(279,365)(280,361)
(281,363)(282,362)(283,367)(284,369)(285,368)(286,370)(287,372)(288,371);;
s1 := (  1,  3)(  4,  6)(  7,  9)( 10, 12)( 13, 21)( 14, 20)( 15, 19)( 16, 24)
( 17, 23)( 18, 22)( 25, 27)( 28, 30)( 31, 33)( 34, 36)( 37, 45)( 38, 44)
( 39, 43)( 40, 48)( 41, 47)( 42, 46)( 49, 54)( 50, 53)( 51, 52)( 55, 60)
( 56, 59)( 57, 58)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)( 66, 67)
( 73, 78)( 74, 77)( 75, 76)( 79, 84)( 80, 83)( 81, 82)( 85, 96)( 86, 95)
( 87, 94)( 88, 93)( 89, 92)( 90, 91)( 97,123)( 98,122)( 99,121)(100,126)
(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)(107,131)(108,130)
(109,141)(110,140)(111,139)(112,144)(113,143)(114,142)(115,135)(116,134)
(117,133)(118,138)(119,137)(120,136)(145,177)(146,176)(147,175)(148,180)
(149,179)(150,178)(151,171)(152,170)(153,169)(154,174)(155,173)(156,172)
(157,183)(158,182)(159,181)(160,186)(161,185)(162,184)(163,189)(164,188)
(165,187)(166,192)(167,191)(168,190)(193,243)(194,242)(195,241)(196,246)
(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)(203,251)(204,250)
(205,261)(206,260)(207,259)(208,264)(209,263)(210,262)(211,255)(212,254)
(213,253)(214,258)(215,257)(216,256)(217,267)(218,266)(219,265)(220,270)
(221,269)(222,268)(223,273)(224,272)(225,271)(226,276)(227,275)(228,274)
(229,285)(230,284)(231,283)(232,288)(233,287)(234,286)(235,279)(236,278)
(237,277)(238,282)(239,281)(240,280)(289,378)(290,377)(291,376)(292,375)
(293,374)(294,373)(295,384)(296,383)(297,382)(298,381)(299,380)(300,379)
(301,369)(302,368)(303,367)(304,372)(305,371)(306,370)(307,363)(308,362)
(309,361)(310,366)(311,365)(312,364)(313,351)(314,350)(315,349)(316,354)
(317,353)(318,352)(319,357)(320,356)(321,355)(322,360)(323,359)(324,358)
(325,348)(326,347)(327,346)(328,345)(329,344)(330,343)(331,342)(332,341)
(333,340)(334,339)(335,338)(336,337);;
s2 := (  1,193)(  2,194)(  3,195)(  4,196)(  5,197)(  6,198)(  7,202)(  8,203)
(  9,204)( 10,199)( 11,200)( 12,201)( 13,205)( 14,206)( 15,207)( 16,208)
( 17,209)( 18,210)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)( 24,213)
( 25,238)( 26,239)( 27,240)( 28,235)( 29,236)( 30,237)( 31,229)( 32,230)
( 33,231)( 34,232)( 35,233)( 36,234)( 37,223)( 38,224)( 39,225)( 40,226)
( 41,227)( 42,228)( 43,220)( 44,221)( 45,222)( 46,217)( 47,218)( 48,219)
( 49,244)( 50,245)( 51,246)( 52,241)( 53,242)( 54,243)( 55,247)( 56,248)
( 57,249)( 58,250)( 59,251)( 60,252)( 61,256)( 62,257)( 63,258)( 64,253)
( 65,254)( 66,255)( 67,259)( 68,260)( 69,261)( 70,262)( 71,263)( 72,264)
( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,280)( 80,281)
( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)( 88,271)
( 89,272)( 90,273)( 91,265)( 92,266)( 93,267)( 94,268)( 95,269)( 96,270)
( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)(104,299)
(105,300)(106,295)(107,296)(108,297)(109,301)(110,302)(111,303)(112,304)
(113,305)(114,306)(115,310)(116,311)(117,312)(118,307)(119,308)(120,309)
(121,334)(122,335)(123,336)(124,331)(125,332)(126,333)(127,325)(128,326)
(129,327)(130,328)(131,329)(132,330)(133,319)(134,320)(135,321)(136,322)
(137,323)(138,324)(139,316)(140,317)(141,318)(142,313)(143,314)(144,315)
(145,340)(146,341)(147,342)(148,337)(149,338)(150,339)(151,343)(152,344)
(153,345)(154,346)(155,347)(156,348)(157,352)(158,353)(159,354)(160,349)
(161,350)(162,351)(163,355)(164,356)(165,357)(166,358)(167,359)(168,360)
(169,379)(170,380)(171,381)(172,382)(173,383)(174,384)(175,376)(176,377)
(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)(184,367)
(185,368)(186,369)(187,361)(188,362)(189,363)(190,364)(191,365)(192,366);;
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*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, 
s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope