Polytope of Type {12,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,16}*768b
if this polytope has a name.
Group : SmallGroup(768,81734)
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
   3-fold quotients : {4,16}*256b
   4-fold quotients : {12,4}*192a, {12,8}*192a, {12,8}*192b
   6-fold quotients : {4,8}*128a
   8-fold quotients : {12,4}*96a, {6,8}*96
   12-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*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, 12)(  8, 11)(  9, 10)( 13, 18)( 14, 17)( 15, 16)
( 19, 21)( 22, 24)( 25, 27)( 28, 30)( 31, 36)( 32, 35)( 33, 34)( 37, 42)
( 38, 41)( 39, 40)( 43, 45)( 46, 48)( 49, 63)( 50, 62)( 51, 61)( 52, 66)
( 53, 65)( 54, 64)( 55, 72)( 56, 71)( 57, 70)( 58, 69)( 59, 68)( 60, 67)
( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)( 78, 88)( 79, 96)( 80, 95)
( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 97,123)( 98,122)( 99,121)(100,126)
(101,125)(102,124)(103,132)(104,131)(105,130)(106,129)(107,128)(108,127)
(109,138)(110,137)(111,136)(112,135)(113,134)(114,133)(115,141)(116,140)
(117,139)(118,144)(119,143)(120,142)(145,186)(146,185)(147,184)(148,183)
(149,182)(150,181)(151,189)(152,188)(153,187)(154,192)(155,191)(156,190)
(157,174)(158,173)(159,172)(160,171)(161,170)(162,169)(163,177)(164,176)
(165,175)(166,180)(167,179)(168,178)(193,243)(194,242)(195,241)(196,246)
(197,245)(198,244)(199,252)(200,251)(201,250)(202,249)(203,248)(204,247)
(205,258)(206,257)(207,256)(208,255)(209,254)(210,253)(211,261)(212,260)
(213,259)(214,264)(215,263)(216,262)(217,267)(218,266)(219,265)(220,270)
(221,269)(222,268)(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)
(229,282)(230,281)(231,280)(232,279)(233,278)(234,277)(235,285)(236,284)
(237,283)(238,288)(239,287)(240,286)(289,369)(290,368)(291,367)(292,372)
(293,371)(294,370)(295,366)(296,365)(297,364)(298,363)(299,362)(300,361)
(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)(307,375)(308,374)
(309,373)(310,378)(311,377)(312,376)(313,345)(314,344)(315,343)(316,348)
(317,347)(318,346)(319,342)(320,341)(321,340)(322,339)(323,338)(324,337)
(325,360)(326,359)(327,358)(328,357)(329,356)(330,355)(331,351)(332,350)
(333,349)(334,354)(335,353)(336,352);;
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)
( 25,226)( 26,227)( 27,228)( 28,223)( 29,224)( 30,225)( 31,220)( 32,221)
( 33,222)( 34,217)( 35,218)( 36,219)( 37,235)( 38,236)( 39,237)( 40,238)
( 41,239)( 42,240)( 43,229)( 44,230)( 45,231)( 46,232)( 47,233)( 48,234)
( 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)
( 73,286)( 74,287)( 75,288)( 76,283)( 77,284)( 78,285)( 79,280)( 80,281)
( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)( 88,271)
( 89,272)( 90,273)( 91,268)( 92,269)( 93,270)( 94,265)( 95,266)( 96,267)
( 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)
(121,322)(122,323)(123,324)(124,319)(125,320)(126,321)(127,316)(128,317)
(129,318)(130,313)(131,314)(132,315)(133,331)(134,332)(135,333)(136,334)
(137,335)(138,336)(139,325)(140,326)(141,327)(142,328)(143,329)(144,330)
(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)
(169,382)(170,383)(171,384)(172,379)(173,380)(174,381)(175,376)(176,377)
(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)(184,367)
(185,368)(186,369)(187,364)(188,365)(189,366)(190,361)(191,362)(192,363);;
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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*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*s0*s1 ];;
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, 12)(  8, 11)(  9, 10)( 13, 18)( 14, 17)
( 15, 16)( 19, 21)( 22, 24)( 25, 27)( 28, 30)( 31, 36)( 32, 35)( 33, 34)
( 37, 42)( 38, 41)( 39, 40)( 43, 45)( 46, 48)( 49, 63)( 50, 62)( 51, 61)
( 52, 66)( 53, 65)( 54, 64)( 55, 72)( 56, 71)( 57, 70)( 58, 69)( 59, 68)
( 60, 67)( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)( 78, 88)( 79, 96)
( 80, 95)( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 97,123)( 98,122)( 99,121)
(100,126)(101,125)(102,124)(103,132)(104,131)(105,130)(106,129)(107,128)
(108,127)(109,138)(110,137)(111,136)(112,135)(113,134)(114,133)(115,141)
(116,140)(117,139)(118,144)(119,143)(120,142)(145,186)(146,185)(147,184)
(148,183)(149,182)(150,181)(151,189)(152,188)(153,187)(154,192)(155,191)
(156,190)(157,174)(158,173)(159,172)(160,171)(161,170)(162,169)(163,177)
(164,176)(165,175)(166,180)(167,179)(168,178)(193,243)(194,242)(195,241)
(196,246)(197,245)(198,244)(199,252)(200,251)(201,250)(202,249)(203,248)
(204,247)(205,258)(206,257)(207,256)(208,255)(209,254)(210,253)(211,261)
(212,260)(213,259)(214,264)(215,263)(216,262)(217,267)(218,266)(219,265)
(220,270)(221,269)(222,268)(223,276)(224,275)(225,274)(226,273)(227,272)
(228,271)(229,282)(230,281)(231,280)(232,279)(233,278)(234,277)(235,285)
(236,284)(237,283)(238,288)(239,287)(240,286)(289,369)(290,368)(291,367)
(292,372)(293,371)(294,370)(295,366)(296,365)(297,364)(298,363)(299,362)
(300,361)(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)(307,375)
(308,374)(309,373)(310,378)(311,377)(312,376)(313,345)(314,344)(315,343)
(316,348)(317,347)(318,346)(319,342)(320,341)(321,340)(322,339)(323,338)
(324,337)(325,360)(326,359)(327,358)(328,357)(329,356)(330,355)(331,351)
(332,350)(333,349)(334,354)(335,353)(336,352);
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)( 25,226)( 26,227)( 27,228)( 28,223)( 29,224)( 30,225)( 31,220)
( 32,221)( 33,222)( 34,217)( 35,218)( 36,219)( 37,235)( 38,236)( 39,237)
( 40,238)( 41,239)( 42,240)( 43,229)( 44,230)( 45,231)( 46,232)( 47,233)
( 48,234)( 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)( 73,286)( 74,287)( 75,288)( 76,283)( 77,284)( 78,285)( 79,280)
( 80,281)( 81,282)( 82,277)( 83,278)( 84,279)( 85,274)( 86,275)( 87,276)
( 88,271)( 89,272)( 90,273)( 91,268)( 92,269)( 93,270)( 94,265)( 95,266)
( 96,267)( 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)(121,322)(122,323)(123,324)(124,319)(125,320)(126,321)(127,316)
(128,317)(129,318)(130,313)(131,314)(132,315)(133,331)(134,332)(135,333)
(136,334)(137,335)(138,336)(139,325)(140,326)(141,327)(142,328)(143,329)
(144,330)(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)(169,382)(170,383)(171,384)(172,379)(173,380)(174,381)(175,376)
(176,377)(177,378)(178,373)(179,374)(180,375)(181,370)(182,371)(183,372)
(184,367)(185,368)(186,369)(187,364)(188,365)(189,366)(190,361)(191,362)
(192,363);
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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*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*s0*s1 >;

References : None.
to this polytope