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Polytope of Type {12,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,16}*768a
if this polytope has a name.
Group : SmallGroup(768,81666)
Rank : 3
Schlafli Type : {12,16}
Number of vertices, edges, etc : 24, 192, 32
Order of s0s1s2 : 48
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {12,8}*384a, {12,16}*384a, {12,16}*384b
   3-fold quotients : {4,16}*256a
   4-fold quotients : {12,4}*192a, {12,8}*192a, {12,8}*192b, {6,16}*192
   6-fold quotients : {4,8}*128a, {4,16}*128a, {4,16}*128b
   8-fold quotients : {12,4}*96a, {6,8}*96
   12-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64, {2,16}*64
   16-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {4,4}*32, {2,8}*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)(  7,103)(  8,105)
(  9,104)( 10,106)( 11,108)( 12,107)( 13,109)( 14,111)( 15,110)( 16,112)
( 17,114)( 18,113)( 19,115)( 20,117)( 21,116)( 22,118)( 23,120)( 24,119)
( 25,121)( 26,123)( 27,122)( 28,124)( 29,126)( 30,125)( 31,127)( 32,129)
( 33,128)( 34,130)( 35,132)( 36,131)( 37,133)( 38,135)( 39,134)( 40,136)
( 41,138)( 42,137)( 43,139)( 44,141)( 45,140)( 46,142)( 47,144)( 48,143)
( 49,151)( 50,153)( 51,152)( 52,154)( 53,156)( 54,155)( 55,145)( 56,147)
( 57,146)( 58,148)( 59,150)( 60,149)( 61,163)( 62,165)( 63,164)( 64,166)
( 65,168)( 66,167)( 67,157)( 68,159)( 69,158)( 70,160)( 71,162)( 72,161)
( 73,175)( 74,177)( 75,176)( 76,178)( 77,180)( 78,179)( 79,169)( 80,171)
( 81,170)( 82,172)( 83,174)( 84,173)( 85,187)( 86,189)( 87,188)( 88,190)
( 89,192)( 90,191)( 91,181)( 92,183)( 93,182)( 94,184)( 95,186)( 96,185)
(193,289)(194,291)(195,290)(196,292)(197,294)(198,293)(199,295)(200,297)
(201,296)(202,298)(203,300)(204,299)(205,301)(206,303)(207,302)(208,304)
(209,306)(210,305)(211,307)(212,309)(213,308)(214,310)(215,312)(216,311)
(217,313)(218,315)(219,314)(220,316)(221,318)(222,317)(223,319)(224,321)
(225,320)(226,322)(227,324)(228,323)(229,325)(230,327)(231,326)(232,328)
(233,330)(234,329)(235,331)(236,333)(237,332)(238,334)(239,336)(240,335)
(241,343)(242,345)(243,344)(244,346)(245,348)(246,347)(247,337)(248,339)
(249,338)(250,340)(251,342)(252,341)(253,355)(254,357)(255,356)(256,358)
(257,360)(258,359)(259,349)(260,351)(261,350)(262,352)(263,354)(264,353)
(265,367)(266,369)(267,368)(268,370)(269,372)(270,371)(271,361)(272,363)
(273,362)(274,364)(275,366)(276,365)(277,379)(278,381)(279,380)(280,382)
(281,384)(282,383)(283,373)(284,375)(285,374)(286,376)(287,378)(288,377);;
s1 := (  1,  3)(  4,  6)(  7,  9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)( 19, 24)
( 20, 23)( 21, 22)( 25, 27)( 28, 30)( 31, 33)( 34, 36)( 37, 42)( 38, 41)
( 39, 40)( 43, 48)( 44, 47)( 45, 46)( 49, 63)( 50, 62)( 51, 61)( 52, 66)
( 53, 65)( 54, 64)( 55, 69)( 56, 68)( 57, 67)( 58, 72)( 59, 71)( 60, 70)
( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)( 78, 88)( 79, 93)( 80, 92)
( 81, 91)( 82, 96)( 83, 95)( 84, 94)( 97,123)( 98,122)( 99,121)(100,126)
(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)(107,131)(108,130)
(109,138)(110,137)(111,136)(112,135)(113,134)(114,133)(115,144)(116,143)
(117,142)(118,141)(119,140)(120,139)(145,183)(146,182)(147,181)(148,186)
(149,185)(150,184)(151,189)(152,188)(153,187)(154,192)(155,191)(156,190)
(157,171)(158,170)(159,169)(160,174)(161,173)(162,172)(163,177)(164,176)
(165,175)(166,180)(167,179)(168,178)(193,243)(194,242)(195,241)(196,246)
(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)(203,251)(204,250)
(205,258)(206,257)(207,256)(208,255)(209,254)(210,253)(211,264)(212,263)
(213,262)(214,261)(215,260)(216,259)(217,267)(218,266)(219,265)(220,270)
(221,269)(222,268)(223,273)(224,272)(225,271)(226,276)(227,275)(228,274)
(229,282)(230,281)(231,280)(232,279)(233,278)(234,277)(235,288)(236,287)
(237,286)(238,285)(239,284)(240,283)(289,369)(290,368)(291,367)(292,372)
(293,371)(294,370)(295,363)(296,362)(297,361)(298,366)(299,365)(300,364)
(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)(307,378)(308,377)
(309,376)(310,375)(311,374)(312,373)(313,345)(314,344)(315,343)(316,348)
(317,347)(318,346)(319,339)(320,338)(321,337)(322,342)(323,341)(324,340)
(325,360)(326,359)(327,358)(328,357)(329,356)(330,355)(331,354)(332,353)
(333,352)(334,351)(335,350)(336,349);;
s2 := (  1,193)(  2,194)(  3,195)(  4,196)(  5,197)(  6,198)(  7,199)(  8,200)
(  9,201)( 10,202)( 11,203)( 12,204)( 13,208)( 14,209)( 15,210)( 16,205)
( 17,206)( 18,207)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)( 24,213)
( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,217)( 32,218)
( 33,219)( 34,220)( 35,221)( 36,222)( 37,238)( 38,239)( 39,240)( 40,235)
( 41,236)( 42,237)( 43,232)( 44,233)( 45,234)( 46,229)( 47,230)( 48,231)
( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,259)( 56,260)
( 57,261)( 58,262)( 59,263)( 60,264)( 61,241)( 62,242)( 63,243)( 64,244)
( 65,245)( 66,246)( 67,247)( 68,248)( 69,249)( 70,250)( 71,251)( 72,252)
( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,277)( 80,278)
( 81,279)( 82,280)( 83,281)( 84,282)( 85,271)( 86,272)( 87,273)( 88,274)
( 89,275)( 90,276)( 91,265)( 92,266)( 93,267)( 94,268)( 95,269)( 96,270)
( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,295)(104,296)
(105,297)(106,298)(107,299)(108,300)(109,304)(110,305)(111,306)(112,301)
(113,302)(114,303)(115,310)(116,311)(117,312)(118,307)(119,308)(120,309)
(121,319)(122,320)(123,321)(124,322)(125,323)(126,324)(127,313)(128,314)
(129,315)(130,316)(131,317)(132,318)(133,334)(134,335)(135,336)(136,331)
(137,332)(138,333)(139,328)(140,329)(141,330)(142,325)(143,326)(144,327)
(145,349)(146,350)(147,351)(148,352)(149,353)(150,354)(151,355)(152,356)
(153,357)(154,358)(155,359)(156,360)(157,337)(158,338)(159,339)(160,340)
(161,341)(162,342)(163,343)(164,344)(165,345)(166,346)(167,347)(168,348)
(169,379)(170,380)(171,381)(172,382)(173,383)(174,384)(175,373)(176,374)
(177,375)(178,376)(179,377)(180,378)(181,367)(182,368)(183,369)(184,370)
(185,371)(186,372)(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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!(  1, 97)(  2, 99)(  3, 98)(  4,100)(  5,102)(  6,101)(  7,103)
(  8,105)(  9,104)( 10,106)( 11,108)( 12,107)( 13,109)( 14,111)( 15,110)
( 16,112)( 17,114)( 18,113)( 19,115)( 20,117)( 21,116)( 22,118)( 23,120)
( 24,119)( 25,121)( 26,123)( 27,122)( 28,124)( 29,126)( 30,125)( 31,127)
( 32,129)( 33,128)( 34,130)( 35,132)( 36,131)( 37,133)( 38,135)( 39,134)
( 40,136)( 41,138)( 42,137)( 43,139)( 44,141)( 45,140)( 46,142)( 47,144)
( 48,143)( 49,151)( 50,153)( 51,152)( 52,154)( 53,156)( 54,155)( 55,145)
( 56,147)( 57,146)( 58,148)( 59,150)( 60,149)( 61,163)( 62,165)( 63,164)
( 64,166)( 65,168)( 66,167)( 67,157)( 68,159)( 69,158)( 70,160)( 71,162)
( 72,161)( 73,175)( 74,177)( 75,176)( 76,178)( 77,180)( 78,179)( 79,169)
( 80,171)( 81,170)( 82,172)( 83,174)( 84,173)( 85,187)( 86,189)( 87,188)
( 88,190)( 89,192)( 90,191)( 91,181)( 92,183)( 93,182)( 94,184)( 95,186)
( 96,185)(193,289)(194,291)(195,290)(196,292)(197,294)(198,293)(199,295)
(200,297)(201,296)(202,298)(203,300)(204,299)(205,301)(206,303)(207,302)
(208,304)(209,306)(210,305)(211,307)(212,309)(213,308)(214,310)(215,312)
(216,311)(217,313)(218,315)(219,314)(220,316)(221,318)(222,317)(223,319)
(224,321)(225,320)(226,322)(227,324)(228,323)(229,325)(230,327)(231,326)
(232,328)(233,330)(234,329)(235,331)(236,333)(237,332)(238,334)(239,336)
(240,335)(241,343)(242,345)(243,344)(244,346)(245,348)(246,347)(247,337)
(248,339)(249,338)(250,340)(251,342)(252,341)(253,355)(254,357)(255,356)
(256,358)(257,360)(258,359)(259,349)(260,351)(261,350)(262,352)(263,354)
(264,353)(265,367)(266,369)(267,368)(268,370)(269,372)(270,371)(271,361)
(272,363)(273,362)(274,364)(275,366)(276,365)(277,379)(278,381)(279,380)
(280,382)(281,384)(282,383)(283,373)(284,375)(285,374)(286,376)(287,378)
(288,377);
s1 := Sym(384)!(  1,  3)(  4,  6)(  7,  9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)
( 19, 24)( 20, 23)( 21, 22)( 25, 27)( 28, 30)( 31, 33)( 34, 36)( 37, 42)
( 38, 41)( 39, 40)( 43, 48)( 44, 47)( 45, 46)( 49, 63)( 50, 62)( 51, 61)
( 52, 66)( 53, 65)( 54, 64)( 55, 69)( 56, 68)( 57, 67)( 58, 72)( 59, 71)
( 60, 70)( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)( 78, 88)( 79, 93)
( 80, 92)( 81, 91)( 82, 96)( 83, 95)( 84, 94)( 97,123)( 98,122)( 99,121)
(100,126)(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)(107,131)
(108,130)(109,138)(110,137)(111,136)(112,135)(113,134)(114,133)(115,144)
(116,143)(117,142)(118,141)(119,140)(120,139)(145,183)(146,182)(147,181)
(148,186)(149,185)(150,184)(151,189)(152,188)(153,187)(154,192)(155,191)
(156,190)(157,171)(158,170)(159,169)(160,174)(161,173)(162,172)(163,177)
(164,176)(165,175)(166,180)(167,179)(168,178)(193,243)(194,242)(195,241)
(196,246)(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)(203,251)
(204,250)(205,258)(206,257)(207,256)(208,255)(209,254)(210,253)(211,264)
(212,263)(213,262)(214,261)(215,260)(216,259)(217,267)(218,266)(219,265)
(220,270)(221,269)(222,268)(223,273)(224,272)(225,271)(226,276)(227,275)
(228,274)(229,282)(230,281)(231,280)(232,279)(233,278)(234,277)(235,288)
(236,287)(237,286)(238,285)(239,284)(240,283)(289,369)(290,368)(291,367)
(292,372)(293,371)(294,370)(295,363)(296,362)(297,361)(298,366)(299,365)
(300,364)(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)(307,378)
(308,377)(309,376)(310,375)(311,374)(312,373)(313,345)(314,344)(315,343)
(316,348)(317,347)(318,346)(319,339)(320,338)(321,337)(322,342)(323,341)
(324,340)(325,360)(326,359)(327,358)(328,357)(329,356)(330,355)(331,354)
(332,353)(333,352)(334,351)(335,350)(336,349);
s2 := Sym(384)!(  1,193)(  2,194)(  3,195)(  4,196)(  5,197)(  6,198)(  7,199)
(  8,200)(  9,201)( 10,202)( 11,203)( 12,204)( 13,208)( 14,209)( 15,210)
( 16,205)( 17,206)( 18,207)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)
( 24,213)( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,217)
( 32,218)( 33,219)( 34,220)( 35,221)( 36,222)( 37,238)( 38,239)( 39,240)
( 40,235)( 41,236)( 42,237)( 43,232)( 44,233)( 45,234)( 46,229)( 47,230)
( 48,231)( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,259)
( 56,260)( 57,261)( 58,262)( 59,263)( 60,264)( 61,241)( 62,242)( 63,243)
( 64,244)( 65,245)( 66,246)( 67,247)( 68,248)( 69,249)( 70,250)( 71,251)
( 72,252)( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,277)
( 80,278)( 81,279)( 82,280)( 83,281)( 84,282)( 85,271)( 86,272)( 87,273)
( 88,274)( 89,275)( 90,276)( 91,265)( 92,266)( 93,267)( 94,268)( 95,269)
( 96,270)( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,295)
(104,296)(105,297)(106,298)(107,299)(108,300)(109,304)(110,305)(111,306)
(112,301)(113,302)(114,303)(115,310)(116,311)(117,312)(118,307)(119,308)
(120,309)(121,319)(122,320)(123,321)(124,322)(125,323)(126,324)(127,313)
(128,314)(129,315)(130,316)(131,317)(132,318)(133,334)(134,335)(135,336)
(136,331)(137,332)(138,333)(139,328)(140,329)(141,330)(142,325)(143,326)
(144,327)(145,349)(146,350)(147,351)(148,352)(149,353)(150,354)(151,355)
(152,356)(153,357)(154,358)(155,359)(156,360)(157,337)(158,338)(159,339)
(160,340)(161,341)(162,342)(163,343)(164,344)(165,345)(166,346)(167,347)
(168,348)(169,379)(170,380)(171,381)(172,382)(173,383)(174,384)(175,373)
(176,374)(177,375)(178,376)(179,377)(180,378)(181,367)(182,368)(183,369)
(184,370)(185,371)(186,372)(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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope