Polytope of Type {4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*768g
if this polytope has a name.
Group : SmallGroup(768,1086024)
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
   Non-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}*384c
   4-fold quotients : {4,6}*192a
   8-fold quotients : {4,12}*96c
   16-fold quotients : {4,6}*48c
   32-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope