Polytope of Type {24,4}

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

References : None.
to this polytope