Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*768o
if this polytope has a name.
Group : SmallGroup(768,1086745)
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 : {6,8}*384g, {12,4}*384e
   4-fold quotients : {6,4}*192b
   8-fold quotients : {6,8}*96, {6,4}*96
   16-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   24-fold quotients : {2,8}*32
   32-fold quotients : {3,4}*24, {6,2}*24
   48-fold quotients : {2,4}*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 := (  3,  4)(  5,  7)(  6,  8)(  9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)
( 14, 24)( 15, 21)( 16, 22)( 27, 28)( 29, 31)( 30, 32)( 33, 41)( 34, 42)
( 35, 44)( 36, 43)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 51, 52)( 53, 55)
( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)( 63, 69)
( 64, 70)( 75, 76)( 77, 79)( 78, 80)( 81, 89)( 82, 90)( 83, 92)( 84, 91)
( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 97, 98)(101,104)(102,103)(105,114)
(106,113)(107,115)(108,116)(109,120)(110,119)(111,118)(112,117)(121,122)
(125,128)(126,127)(129,138)(130,137)(131,139)(132,140)(133,144)(134,143)
(135,142)(136,141)(145,146)(149,152)(150,151)(153,162)(154,161)(155,163)
(156,164)(157,168)(158,167)(159,166)(160,165)(169,170)(173,176)(174,175)
(177,186)(178,185)(179,187)(180,188)(181,192)(182,191)(183,190)(184,189)
(193,194)(197,200)(198,199)(201,210)(202,209)(203,211)(204,212)(205,216)
(206,215)(207,214)(208,213)(217,218)(221,224)(222,223)(225,234)(226,233)
(227,235)(228,236)(229,240)(230,239)(231,238)(232,237)(241,242)(245,248)
(246,247)(249,258)(250,257)(251,259)(252,260)(253,264)(254,263)(255,262)
(256,261)(265,266)(269,272)(270,271)(273,282)(274,281)(275,283)(276,284)
(277,288)(278,287)(279,286)(280,285)(291,292)(293,295)(294,296)(297,305)
(298,306)(299,308)(300,307)(301,311)(302,312)(303,309)(304,310)(315,316)
(317,319)(318,320)(321,329)(322,330)(323,332)(324,331)(325,335)(326,336)
(327,333)(328,334)(339,340)(341,343)(342,344)(345,353)(346,354)(347,356)
(348,355)(349,359)(350,360)(351,357)(352,358)(363,364)(365,367)(366,368)
(369,377)(370,378)(371,380)(372,379)(373,383)(374,384)(375,381)(376,382);;
s1 := (  1,209)(  2,210)(  3,214)(  4,213)(  5,212)(  6,211)(  7,216)(  8,215)
(  9,201)( 10,202)( 11,206)( 12,205)( 13,204)( 14,203)( 15,208)( 16,207)
( 17,193)( 18,194)( 19,198)( 20,197)( 21,196)( 22,195)( 23,200)( 24,199)
( 25,233)( 26,234)( 27,238)( 28,237)( 29,236)( 30,235)( 31,240)( 32,239)
( 33,225)( 34,226)( 35,230)( 36,229)( 37,228)( 38,227)( 39,232)( 40,231)
( 41,217)( 42,218)( 43,222)( 44,221)( 45,220)( 46,219)( 47,224)( 48,223)
( 49,281)( 50,282)( 51,286)( 52,285)( 53,284)( 54,283)( 55,288)( 56,287)
( 57,273)( 58,274)( 59,278)( 60,277)( 61,276)( 62,275)( 63,280)( 64,279)
( 65,265)( 66,266)( 67,270)( 68,269)( 69,268)( 70,267)( 71,272)( 72,271)
( 73,257)( 74,258)( 75,262)( 76,261)( 77,260)( 78,259)( 79,264)( 80,263)
( 81,249)( 82,250)( 83,254)( 84,253)( 85,252)( 86,251)( 87,256)( 88,255)
( 89,241)( 90,242)( 91,246)( 92,245)( 93,244)( 94,243)( 95,248)( 96,247)
( 97,354)( 98,353)( 99,357)(100,358)(101,355)(102,356)(103,359)(104,360)
(105,346)(106,345)(107,349)(108,350)(109,347)(110,348)(111,351)(112,352)
(113,338)(114,337)(115,341)(116,342)(117,339)(118,340)(119,343)(120,344)
(121,378)(122,377)(123,381)(124,382)(125,379)(126,380)(127,383)(128,384)
(129,370)(130,369)(131,373)(132,374)(133,371)(134,372)(135,375)(136,376)
(137,362)(138,361)(139,365)(140,366)(141,363)(142,364)(143,367)(144,368)
(145,306)(146,305)(147,309)(148,310)(149,307)(150,308)(151,311)(152,312)
(153,298)(154,297)(155,301)(156,302)(157,299)(158,300)(159,303)(160,304)
(161,290)(162,289)(163,293)(164,294)(165,291)(166,292)(167,295)(168,296)
(169,330)(170,329)(171,333)(172,334)(173,331)(174,332)(175,335)(176,336)
(177,322)(178,321)(179,325)(180,326)(181,323)(182,324)(183,327)(184,328)
(185,314)(186,313)(187,317)(188,318)(189,315)(190,316)(191,319)(192,320);;
s2 := (  1,100)(  2, 99)(  3, 97)(  4, 98)(  5,104)(  6,103)(  7,101)(  8,102)
(  9,108)( 10,107)( 11,105)( 12,106)( 13,112)( 14,111)( 15,109)( 16,110)
( 17,116)( 18,115)( 19,113)( 20,114)( 21,120)( 22,119)( 23,117)( 24,118)
( 25,124)( 26,123)( 27,121)( 28,122)( 29,128)( 30,127)( 31,125)( 32,126)
( 33,132)( 34,131)( 35,129)( 36,130)( 37,136)( 38,135)( 39,133)( 40,134)
( 41,140)( 42,139)( 43,137)( 44,138)( 45,144)( 46,143)( 47,141)( 48,142)
( 49,172)( 50,171)( 51,169)( 52,170)( 53,176)( 54,175)( 55,173)( 56,174)
( 57,180)( 58,179)( 59,177)( 60,178)( 61,184)( 62,183)( 63,181)( 64,182)
( 65,188)( 66,187)( 67,185)( 68,186)( 69,192)( 70,191)( 71,189)( 72,190)
( 73,148)( 74,147)( 75,145)( 76,146)( 77,152)( 78,151)( 79,149)( 80,150)
( 81,156)( 82,155)( 83,153)( 84,154)( 85,160)( 86,159)( 87,157)( 88,158)
( 89,164)( 90,163)( 91,161)( 92,162)( 93,168)( 94,167)( 95,165)( 96,166)
(193,292)(194,291)(195,289)(196,290)(197,296)(198,295)(199,293)(200,294)
(201,300)(202,299)(203,297)(204,298)(205,304)(206,303)(207,301)(208,302)
(209,308)(210,307)(211,305)(212,306)(213,312)(214,311)(215,309)(216,310)
(217,316)(218,315)(219,313)(220,314)(221,320)(222,319)(223,317)(224,318)
(225,324)(226,323)(227,321)(228,322)(229,328)(230,327)(231,325)(232,326)
(233,332)(234,331)(235,329)(236,330)(237,336)(238,335)(239,333)(240,334)
(241,364)(242,363)(243,361)(244,362)(245,368)(246,367)(247,365)(248,366)
(249,372)(250,371)(251,369)(252,370)(253,376)(254,375)(255,373)(256,374)
(257,380)(258,379)(259,377)(260,378)(261,384)(262,383)(263,381)(264,382)
(265,340)(266,339)(267,337)(268,338)(269,344)(270,343)(271,341)(272,342)
(273,348)(274,347)(275,345)(276,346)(277,352)(278,351)(279,349)(280,350)
(281,356)(282,355)(283,353)(284,354)(285,360)(286,359)(287,357)(288,358);;
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, 
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope