Polytope of Type {24,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*768g
if this polytope has a name.
Group : SmallGroup(768,1086024)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 96, 192, 16
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*384c
   4-fold quotients : {6,4}*192a
   8-fold quotients : {12,4}*96c
   16-fold quotients : {6,4}*48c
   32-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope