Polytope of Type {12,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*768a
if this polytope has a name.
Group : SmallGroup(768,1086745)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 16, 192, 32
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 12
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 : {12,12}*384c, {6,24}*384a
   4-fold quotients : {6,12}*192a, {12,6}*192b
   8-fold quotients : {12,3}*96, {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   24-fold quotients : {2,8}*32
   32-fold quotients : {3,3}*24
   48-fold quotients : {2,4}*16
   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, 99)(  2,100)(  3, 97)(  4, 98)(  5,102)(  6,101)(  7,103)(  8,104)
(  9,115)( 10,116)( 11,113)( 12,114)( 13,118)( 14,117)( 15,119)( 16,120)
( 17,107)( 18,108)( 19,105)( 20,106)( 21,110)( 22,109)( 23,111)( 24,112)
( 25,123)( 26,124)( 27,121)( 28,122)( 29,126)( 30,125)( 31,127)( 32,128)
( 33,139)( 34,140)( 35,137)( 36,138)( 37,142)( 38,141)( 39,143)( 40,144)
( 41,131)( 42,132)( 43,129)( 44,130)( 45,134)( 46,133)( 47,135)( 48,136)
( 49,171)( 50,172)( 51,169)( 52,170)( 53,174)( 54,173)( 55,175)( 56,176)
( 57,187)( 58,188)( 59,185)( 60,186)( 61,190)( 62,189)( 63,191)( 64,192)
( 65,179)( 66,180)( 67,177)( 68,178)( 69,182)( 70,181)( 71,183)( 72,184)
( 73,147)( 74,148)( 75,145)( 76,146)( 77,150)( 78,149)( 79,151)( 80,152)
( 81,163)( 82,164)( 83,161)( 84,162)( 85,166)( 86,165)( 87,167)( 88,168)
( 89,155)( 90,156)( 91,153)( 92,154)( 93,158)( 94,157)( 95,159)( 96,160)
(193,292)(194,291)(195,290)(196,289)(197,293)(198,294)(199,296)(200,295)
(201,308)(202,307)(203,306)(204,305)(205,309)(206,310)(207,312)(208,311)
(209,300)(210,299)(211,298)(212,297)(213,301)(214,302)(215,304)(216,303)
(217,316)(218,315)(219,314)(220,313)(221,317)(222,318)(223,320)(224,319)
(225,332)(226,331)(227,330)(228,329)(229,333)(230,334)(231,336)(232,335)
(233,324)(234,323)(235,322)(236,321)(237,325)(238,326)(239,328)(240,327)
(241,364)(242,363)(243,362)(244,361)(245,365)(246,366)(247,368)(248,367)
(249,380)(250,379)(251,378)(252,377)(253,381)(254,382)(255,384)(256,383)
(257,372)(258,371)(259,370)(260,369)(261,373)(262,374)(263,376)(264,375)
(265,340)(266,339)(267,338)(268,337)(269,341)(270,342)(271,344)(272,343)
(273,356)(274,355)(275,354)(276,353)(277,357)(278,358)(279,360)(280,359)
(281,348)(282,347)(283,346)(284,345)(285,349)(286,350)(287,352)(288,351);;
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*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1 ];;
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, 99)(  2,100)(  3, 97)(  4, 98)(  5,102)(  6,101)(  7,103)
(  8,104)(  9,115)( 10,116)( 11,113)( 12,114)( 13,118)( 14,117)( 15,119)
( 16,120)( 17,107)( 18,108)( 19,105)( 20,106)( 21,110)( 22,109)( 23,111)
( 24,112)( 25,123)( 26,124)( 27,121)( 28,122)( 29,126)( 30,125)( 31,127)
( 32,128)( 33,139)( 34,140)( 35,137)( 36,138)( 37,142)( 38,141)( 39,143)
( 40,144)( 41,131)( 42,132)( 43,129)( 44,130)( 45,134)( 46,133)( 47,135)
( 48,136)( 49,171)( 50,172)( 51,169)( 52,170)( 53,174)( 54,173)( 55,175)
( 56,176)( 57,187)( 58,188)( 59,185)( 60,186)( 61,190)( 62,189)( 63,191)
( 64,192)( 65,179)( 66,180)( 67,177)( 68,178)( 69,182)( 70,181)( 71,183)
( 72,184)( 73,147)( 74,148)( 75,145)( 76,146)( 77,150)( 78,149)( 79,151)
( 80,152)( 81,163)( 82,164)( 83,161)( 84,162)( 85,166)( 86,165)( 87,167)
( 88,168)( 89,155)( 90,156)( 91,153)( 92,154)( 93,158)( 94,157)( 95,159)
( 96,160)(193,292)(194,291)(195,290)(196,289)(197,293)(198,294)(199,296)
(200,295)(201,308)(202,307)(203,306)(204,305)(205,309)(206,310)(207,312)
(208,311)(209,300)(210,299)(211,298)(212,297)(213,301)(214,302)(215,304)
(216,303)(217,316)(218,315)(219,314)(220,313)(221,317)(222,318)(223,320)
(224,319)(225,332)(226,331)(227,330)(228,329)(229,333)(230,334)(231,336)
(232,335)(233,324)(234,323)(235,322)(236,321)(237,325)(238,326)(239,328)
(240,327)(241,364)(242,363)(243,362)(244,361)(245,365)(246,366)(247,368)
(248,367)(249,380)(250,379)(251,378)(252,377)(253,381)(254,382)(255,384)
(256,383)(257,372)(258,371)(259,370)(260,369)(261,373)(262,374)(263,376)
(264,375)(265,340)(266,339)(267,338)(268,337)(269,341)(270,342)(271,344)
(272,343)(273,356)(274,355)(275,354)(276,353)(277,357)(278,358)(279,360)
(280,359)(281,348)(282,347)(283,346)(284,345)(285,349)(286,350)(287,352)
(288,351);
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*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
to this polytope