Polytope of Type {4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*768c
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 : {4,12}*384a
   3-fold quotients : {4,8}*256c
   4-fold quotients : {4,12}*192a
   6-fold quotients : {4,4}*128
   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 := (  1,195)(  2,194)(  3,193)(  4,198)(  5,197)(  6,196)(  7,204)(  8,203)
(  9,202)( 10,201)( 11,200)( 12,199)( 13,207)( 14,206)( 15,205)( 16,210)
( 17,209)( 18,208)( 19,216)( 20,215)( 21,214)( 22,213)( 23,212)( 24,211)
( 25,240)( 26,239)( 27,238)( 28,237)( 29,236)( 30,235)( 31,231)( 32,230)
( 33,229)( 34,234)( 35,233)( 36,232)( 37,225)( 38,224)( 39,223)( 40,228)
( 41,227)( 42,226)( 43,222)( 44,221)( 45,220)( 46,219)( 47,218)( 48,217)
( 49,246)( 50,245)( 51,244)( 52,243)( 53,242)( 54,241)( 55,249)( 56,248)
( 57,247)( 58,252)( 59,251)( 60,250)( 61,258)( 62,257)( 63,256)( 64,255)
( 65,254)( 66,253)( 67,261)( 68,260)( 69,259)( 70,264)( 71,263)( 72,262)
( 73,285)( 74,284)( 75,283)( 76,288)( 77,287)( 78,286)( 79,282)( 80,281)
( 81,280)( 82,279)( 83,278)( 84,277)( 85,276)( 86,275)( 87,274)( 88,273)
( 89,272)( 90,271)( 91,267)( 92,266)( 93,265)( 94,270)( 95,269)( 96,268)
( 97,291)( 98,290)( 99,289)(100,294)(101,293)(102,292)(103,300)(104,299)
(105,298)(106,297)(107,296)(108,295)(109,303)(110,302)(111,301)(112,306)
(113,305)(114,304)(115,312)(116,311)(117,310)(118,309)(119,308)(120,307)
(121,336)(122,335)(123,334)(124,333)(125,332)(126,331)(127,327)(128,326)
(129,325)(130,330)(131,329)(132,328)(133,321)(134,320)(135,319)(136,324)
(137,323)(138,322)(139,318)(140,317)(141,316)(142,315)(143,314)(144,313)
(145,342)(146,341)(147,340)(148,339)(149,338)(150,337)(151,345)(152,344)
(153,343)(154,348)(155,347)(156,346)(157,354)(158,353)(159,352)(160,351)
(161,350)(162,349)(163,357)(164,356)(165,355)(166,360)(167,359)(168,358)
(169,381)(170,380)(171,379)(172,384)(173,383)(174,382)(175,378)(176,377)
(177,376)(178,375)(179,374)(180,373)(181,372)(182,371)(183,370)(184,369)
(185,368)(186,367)(187,363)(188,362)(189,361)(190,366)(191,365)(192,364);;
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, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2 ];;
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)!(  1,195)(  2,194)(  3,193)(  4,198)(  5,197)(  6,196)(  7,204)
(  8,203)(  9,202)( 10,201)( 11,200)( 12,199)( 13,207)( 14,206)( 15,205)
( 16,210)( 17,209)( 18,208)( 19,216)( 20,215)( 21,214)( 22,213)( 23,212)
( 24,211)( 25,240)( 26,239)( 27,238)( 28,237)( 29,236)( 30,235)( 31,231)
( 32,230)( 33,229)( 34,234)( 35,233)( 36,232)( 37,225)( 38,224)( 39,223)
( 40,228)( 41,227)( 42,226)( 43,222)( 44,221)( 45,220)( 46,219)( 47,218)
( 48,217)( 49,246)( 50,245)( 51,244)( 52,243)( 53,242)( 54,241)( 55,249)
( 56,248)( 57,247)( 58,252)( 59,251)( 60,250)( 61,258)( 62,257)( 63,256)
( 64,255)( 65,254)( 66,253)( 67,261)( 68,260)( 69,259)( 70,264)( 71,263)
( 72,262)( 73,285)( 74,284)( 75,283)( 76,288)( 77,287)( 78,286)( 79,282)
( 80,281)( 81,280)( 82,279)( 83,278)( 84,277)( 85,276)( 86,275)( 87,274)
( 88,273)( 89,272)( 90,271)( 91,267)( 92,266)( 93,265)( 94,270)( 95,269)
( 96,268)( 97,291)( 98,290)( 99,289)(100,294)(101,293)(102,292)(103,300)
(104,299)(105,298)(106,297)(107,296)(108,295)(109,303)(110,302)(111,301)
(112,306)(113,305)(114,304)(115,312)(116,311)(117,310)(118,309)(119,308)
(120,307)(121,336)(122,335)(123,334)(124,333)(125,332)(126,331)(127,327)
(128,326)(129,325)(130,330)(131,329)(132,328)(133,321)(134,320)(135,319)
(136,324)(137,323)(138,322)(139,318)(140,317)(141,316)(142,315)(143,314)
(144,313)(145,342)(146,341)(147,340)(148,339)(149,338)(150,337)(151,345)
(152,344)(153,343)(154,348)(155,347)(156,346)(157,354)(158,353)(159,352)
(160,351)(161,350)(162,349)(163,357)(164,356)(165,355)(166,360)(167,359)
(168,358)(169,381)(170,380)(171,379)(172,384)(173,383)(174,382)(175,378)
(176,377)(177,376)(178,375)(179,374)(180,373)(181,372)(182,371)(183,370)
(184,369)(185,368)(186,367)(187,363)(188,362)(189,361)(190,366)(191,365)
(192,364);
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, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2 >;

References : None.
to this polytope