Polytope of Type {24,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*768a
if this polytope has a name.
Group : SmallGroup(768,1086745)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 32, 192, 16
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}*384d, {24,6}*384a
   4-fold quotients : {12,6}*192a, {6,12}*192b
   8-fold quotients : {3,12}*96, {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   24-fold quotients : {8,2}*32
   32-fold quotients : {3,3}*24
   48-fold quotients : {4,2}*16
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope