Polytope of Type {24,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*768e
if this polytope has a name.
Group : SmallGroup(768,1085644)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 96, 192, 16
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*384b
   4-fold quotients : {6,4}*192a, {24,4}*192c
   8-fold quotients : {12,4}*96b
   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 := (  3,  4)(  7,  8)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)
( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)( 55, 56)
( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)( 68, 83)
( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 93)( 74, 94)( 75, 96)( 76, 95)
( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 97,145)( 98,146)( 99,148)(100,147)
(101,149)(102,150)(103,152)(104,151)(105,157)(106,158)(107,160)(108,159)
(109,153)(110,154)(111,156)(112,155)(113,177)(114,178)(115,180)(116,179)
(117,181)(118,182)(119,184)(120,183)(121,189)(122,190)(123,192)(124,191)
(125,185)(126,186)(127,188)(128,187)(129,161)(130,162)(131,164)(132,163)
(133,165)(134,166)(135,168)(136,167)(137,173)(138,174)(139,176)(140,175)
(141,169)(142,170)(143,172)(144,171)(193,289)(194,290)(195,292)(196,291)
(197,293)(198,294)(199,296)(200,295)(201,301)(202,302)(203,304)(204,303)
(205,297)(206,298)(207,300)(208,299)(209,321)(210,322)(211,324)(212,323)
(213,325)(214,326)(215,328)(216,327)(217,333)(218,334)(219,336)(220,335)
(221,329)(222,330)(223,332)(224,331)(225,305)(226,306)(227,308)(228,307)
(229,309)(230,310)(231,312)(232,311)(233,317)(234,318)(235,320)(236,319)
(237,313)(238,314)(239,316)(240,315)(241,337)(242,338)(243,340)(244,339)
(245,341)(246,342)(247,344)(248,343)(249,349)(250,350)(251,352)(252,351)
(253,345)(254,346)(255,348)(256,347)(257,369)(258,370)(259,372)(260,371)
(261,373)(262,374)(263,376)(264,375)(265,381)(266,382)(267,384)(268,383)
(269,377)(270,378)(271,380)(272,379)(273,353)(274,354)(275,356)(276,355)
(277,357)(278,358)(279,360)(280,359)(281,365)(282,366)(283,368)(284,367)
(285,361)(286,362)(287,364)(288,363);;
s1 := (  1,321)(  2,323)(  3,322)(  4,324)(  5,331)(  6,329)(  7,332)(  8,330)
(  9,326)( 10,328)( 11,325)( 12,327)( 13,336)( 14,334)( 15,335)( 16,333)
( 17,305)( 18,307)( 19,306)( 20,308)( 21,315)( 22,313)( 23,316)( 24,314)
( 25,310)( 26,312)( 27,309)( 28,311)( 29,320)( 30,318)( 31,319)( 32,317)
( 33,289)( 34,291)( 35,290)( 36,292)( 37,299)( 38,297)( 39,300)( 40,298)
( 41,294)( 42,296)( 43,293)( 44,295)( 45,304)( 46,302)( 47,303)( 48,301)
( 49,369)( 50,371)( 51,370)( 52,372)( 53,379)( 54,377)( 55,380)( 56,378)
( 57,374)( 58,376)( 59,373)( 60,375)( 61,384)( 62,382)( 63,383)( 64,381)
( 65,353)( 66,355)( 67,354)( 68,356)( 69,363)( 70,361)( 71,364)( 72,362)
( 73,358)( 74,360)( 75,357)( 76,359)( 77,368)( 78,366)( 79,367)( 80,365)
( 81,337)( 82,339)( 83,338)( 84,340)( 85,347)( 86,345)( 87,348)( 88,346)
( 89,342)( 90,344)( 91,341)( 92,343)( 93,352)( 94,350)( 95,351)( 96,349)
( 97,225)( 98,227)( 99,226)(100,228)(101,235)(102,233)(103,236)(104,234)
(105,230)(106,232)(107,229)(108,231)(109,240)(110,238)(111,239)(112,237)
(113,209)(114,211)(115,210)(116,212)(117,219)(118,217)(119,220)(120,218)
(121,214)(122,216)(123,213)(124,215)(125,224)(126,222)(127,223)(128,221)
(129,193)(130,195)(131,194)(132,196)(133,203)(134,201)(135,204)(136,202)
(137,198)(138,200)(139,197)(140,199)(141,208)(142,206)(143,207)(144,205)
(145,273)(146,275)(147,274)(148,276)(149,283)(150,281)(151,284)(152,282)
(153,278)(154,280)(155,277)(156,279)(157,288)(158,286)(159,287)(160,285)
(161,257)(162,259)(163,258)(164,260)(165,267)(166,265)(167,268)(168,266)
(169,262)(170,264)(171,261)(172,263)(173,272)(174,270)(175,271)(176,269)
(177,241)(178,243)(179,242)(180,244)(181,251)(182,249)(183,252)(184,250)
(185,246)(186,248)(187,245)(188,247)(189,256)(190,254)(191,255)(192,253);;
s2 := (  1,  5)(  2,  6)(  3,  7)(  4,  8)(  9, 13)( 10, 14)( 11, 15)( 12, 16)
( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 29)( 26, 30)( 27, 31)( 28, 32)
( 33, 37)( 34, 38)( 35, 39)( 36, 40)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 61)( 58, 62)( 59, 63)( 60, 64)
( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 77)( 74, 78)( 75, 79)( 76, 80)
( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
( 97,101)( 98,102)( 99,103)(100,104)(105,109)(106,110)(107,111)(108,112)
(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)
(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)
(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160)
(161,165)(162,166)(163,167)(164,168)(169,173)(170,174)(171,175)(172,176)
(177,181)(178,182)(179,183)(180,184)(185,189)(186,190)(187,191)(188,192)
(193,197)(194,198)(195,199)(196,200)(201,205)(202,206)(203,207)(204,208)
(209,213)(210,214)(211,215)(212,216)(217,221)(218,222)(219,223)(220,224)
(225,229)(226,230)(227,231)(228,232)(233,237)(234,238)(235,239)(236,240)
(241,245)(242,246)(243,247)(244,248)(249,253)(250,254)(251,255)(252,256)
(257,261)(258,262)(259,263)(260,264)(265,269)(266,270)(267,271)(268,272)
(273,277)(274,278)(275,279)(276,280)(281,285)(282,286)(283,287)(284,288)
(289,293)(290,294)(291,295)(292,296)(297,301)(298,302)(299,303)(300,304)
(305,309)(306,310)(307,311)(308,312)(313,317)(314,318)(315,319)(316,320)
(321,325)(322,326)(323,327)(324,328)(329,333)(330,334)(331,335)(332,336)
(337,341)(338,342)(339,343)(340,344)(345,349)(346,350)(347,351)(348,352)
(353,357)(354,358)(355,359)(356,360)(361,365)(362,366)(363,367)(364,368)
(369,373)(370,374)(371,375)(372,376)(377,381)(378,382)(379,383)(380,384);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope