Polytope of Type {4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*768d
if this polytope has a name.
Group : SmallGroup(768,90302)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 16, 192, 96
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 8
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 : {4,24}*384b
   3-fold quotients : {4,8}*256d
   4-fold quotients : {4,12}*192a
   6-fold quotients : {4,8}*128b
   8-fold quotients : {4,12}*96a
   12-fold quotients : {4,4}*64
   16-fold quotients : {2,12}*48, {4,6}*48a
   24-fold quotients : {4,4}*32
   32-fold quotients : {2,6}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   64-fold quotients : {2,3}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope