Polytope of Type {24,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*768d
if this polytope has a name.
Group : SmallGroup(768,90302)
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
Orientable
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 : {24,4}*384b
3-fold quotients : {8,4}*256d
4-fold quotients : {12,4}*192a
6-fold quotients : {8,4}*128b
8-fold quotients : {12,4}*96a
12-fold quotients : {4,4}*64
16-fold quotients : {12,2}*48, {6,4}*48a
24-fold quotients : {4,4}*32
32-fold quotients : {6,2}*24
48-fold quotients : {2,4}*16, {4,2}*16
64-fold quotients : {3,2}*12
96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,289)( 2,291)( 3,290)( 4,292)( 5,294)( 6,293)( 7,295)( 8,297)
( 9,296)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)( 16,301)
( 17,303)( 18,302)( 19,310)( 20,312)( 21,311)( 22,307)( 23,309)( 24,308)
( 25,334)( 26,336)( 27,335)( 28,331)( 29,333)( 30,332)( 31,328)( 32,330)
( 33,329)( 34,325)( 35,327)( 36,326)( 37,322)( 38,324)( 39,323)( 40,319)
( 41,321)( 42,320)( 43,316)( 44,318)( 45,317)( 46,313)( 47,315)( 48,314)
( 49,352)( 50,354)( 51,353)( 52,349)( 53,351)( 54,350)( 55,358)( 56,360)
( 57,359)( 58,355)( 59,357)( 60,356)( 61,340)( 62,342)( 63,341)( 64,337)
( 65,339)( 66,338)( 67,346)( 68,348)( 69,347)( 70,343)( 71,345)( 72,344)
( 73,367)( 74,369)( 75,368)( 76,370)( 77,372)( 78,371)( 79,361)( 80,363)
( 81,362)( 82,364)( 83,366)( 84,365)( 85,382)( 86,384)( 87,383)( 88,379)
( 89,381)( 90,380)( 91,376)( 92,378)( 93,377)( 94,373)( 95,375)( 96,374)
( 97,193)( 98,195)( 99,194)(100,196)(101,198)(102,197)(103,199)(104,201)
(105,200)(106,202)(107,204)(108,203)(109,208)(110,210)(111,209)(112,205)
(113,207)(114,206)(115,214)(116,216)(117,215)(118,211)(119,213)(120,212)
(121,238)(122,240)(123,239)(124,235)(125,237)(126,236)(127,232)(128,234)
(129,233)(130,229)(131,231)(132,230)(133,226)(134,228)(135,227)(136,223)
(137,225)(138,224)(139,220)(140,222)(141,221)(142,217)(143,219)(144,218)
(145,256)(146,258)(147,257)(148,253)(149,255)(150,254)(151,262)(152,264)
(153,263)(154,259)(155,261)(156,260)(157,244)(158,246)(159,245)(160,241)
(161,243)(162,242)(163,250)(164,252)(165,251)(166,247)(167,249)(168,248)
(169,271)(170,273)(171,272)(172,274)(173,276)(174,275)(175,265)(176,267)
(177,266)(178,268)(179,270)(180,269)(181,286)(182,288)(183,287)(184,283)
(185,285)(186,284)(187,280)(188,282)(189,281)(190,277)(191,279)(192,278);;
s1 := ( 1, 3)( 4, 6)( 7, 9)( 10, 12)( 13, 21)( 14, 20)( 15, 19)( 16, 24)
( 17, 23)( 18, 22)( 25, 27)( 28, 30)( 31, 33)( 34, 36)( 37, 45)( 38, 44)
( 39, 43)( 40, 48)( 41, 47)( 42, 46)( 49, 54)( 50, 53)( 51, 52)( 55, 60)
( 56, 59)( 57, 58)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)( 66, 67)
( 73, 78)( 74, 77)( 75, 76)( 79, 84)( 80, 83)( 81, 82)( 85, 96)( 86, 95)
( 87, 94)( 88, 93)( 89, 92)( 90, 91)( 97,123)( 98,122)( 99,121)(100,126)
(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)(107,131)(108,130)
(109,141)(110,140)(111,139)(112,144)(113,143)(114,142)(115,135)(116,134)
(117,133)(118,138)(119,137)(120,136)(145,177)(146,176)(147,175)(148,180)
(149,179)(150,178)(151,171)(152,170)(153,169)(154,174)(155,173)(156,172)
(157,183)(158,182)(159,181)(160,186)(161,185)(162,184)(163,189)(164,188)
(165,187)(166,192)(167,191)(168,190)(193,243)(194,242)(195,241)(196,246)
(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)(203,251)(204,250)
(205,261)(206,260)(207,259)(208,264)(209,263)(210,262)(211,255)(212,254)
(213,253)(214,258)(215,257)(216,256)(217,267)(218,266)(219,265)(220,270)
(221,269)(222,268)(223,273)(224,272)(225,271)(226,276)(227,275)(228,274)
(229,285)(230,284)(231,283)(232,288)(233,287)(234,286)(235,279)(236,278)
(237,277)(238,282)(239,281)(240,280)(289,378)(290,377)(291,376)(292,375)
(293,374)(294,373)(295,384)(296,383)(297,382)(298,381)(299,380)(300,379)
(301,369)(302,368)(303,367)(304,372)(305,371)(306,370)(307,363)(308,362)
(309,361)(310,366)(311,365)(312,364)(313,351)(314,350)(315,349)(316,354)
(317,353)(318,352)(319,357)(320,356)(321,355)(322,360)(323,359)(324,358)
(325,348)(326,347)(327,346)(328,345)(329,344)(330,343)(331,342)(332,341)
(333,340)(334,339)(335,338)(336,337);;
s2 := ( 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);;
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*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1,289)( 2,291)( 3,290)( 4,292)( 5,294)( 6,293)( 7,295)
( 8,297)( 9,296)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)
( 16,301)( 17,303)( 18,302)( 19,310)( 20,312)( 21,311)( 22,307)( 23,309)
( 24,308)( 25,334)( 26,336)( 27,335)( 28,331)( 29,333)( 30,332)( 31,328)
( 32,330)( 33,329)( 34,325)( 35,327)( 36,326)( 37,322)( 38,324)( 39,323)
( 40,319)( 41,321)( 42,320)( 43,316)( 44,318)( 45,317)( 46,313)( 47,315)
( 48,314)( 49,352)( 50,354)( 51,353)( 52,349)( 53,351)( 54,350)( 55,358)
( 56,360)( 57,359)( 58,355)( 59,357)( 60,356)( 61,340)( 62,342)( 63,341)
( 64,337)( 65,339)( 66,338)( 67,346)( 68,348)( 69,347)( 70,343)( 71,345)
( 72,344)( 73,367)( 74,369)( 75,368)( 76,370)( 77,372)( 78,371)( 79,361)
( 80,363)( 81,362)( 82,364)( 83,366)( 84,365)( 85,382)( 86,384)( 87,383)
( 88,379)( 89,381)( 90,380)( 91,376)( 92,378)( 93,377)( 94,373)( 95,375)
( 96,374)( 97,193)( 98,195)( 99,194)(100,196)(101,198)(102,197)(103,199)
(104,201)(105,200)(106,202)(107,204)(108,203)(109,208)(110,210)(111,209)
(112,205)(113,207)(114,206)(115,214)(116,216)(117,215)(118,211)(119,213)
(120,212)(121,238)(122,240)(123,239)(124,235)(125,237)(126,236)(127,232)
(128,234)(129,233)(130,229)(131,231)(132,230)(133,226)(134,228)(135,227)
(136,223)(137,225)(138,224)(139,220)(140,222)(141,221)(142,217)(143,219)
(144,218)(145,256)(146,258)(147,257)(148,253)(149,255)(150,254)(151,262)
(152,264)(153,263)(154,259)(155,261)(156,260)(157,244)(158,246)(159,245)
(160,241)(161,243)(162,242)(163,250)(164,252)(165,251)(166,247)(167,249)
(168,248)(169,271)(170,273)(171,272)(172,274)(173,276)(174,275)(175,265)
(176,267)(177,266)(178,268)(179,270)(180,269)(181,286)(182,288)(183,287)
(184,283)(185,285)(186,284)(187,280)(188,282)(189,281)(190,277)(191,279)
(192,278);
s1 := Sym(384)!( 1, 3)( 4, 6)( 7, 9)( 10, 12)( 13, 21)( 14, 20)( 15, 19)
( 16, 24)( 17, 23)( 18, 22)( 25, 27)( 28, 30)( 31, 33)( 34, 36)( 37, 45)
( 38, 44)( 39, 43)( 40, 48)( 41, 47)( 42, 46)( 49, 54)( 50, 53)( 51, 52)
( 55, 60)( 56, 59)( 57, 58)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)
( 66, 67)( 73, 78)( 74, 77)( 75, 76)( 79, 84)( 80, 83)( 81, 82)( 85, 96)
( 86, 95)( 87, 94)( 88, 93)( 89, 92)( 90, 91)( 97,123)( 98,122)( 99,121)
(100,126)(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)(107,131)
(108,130)(109,141)(110,140)(111,139)(112,144)(113,143)(114,142)(115,135)
(116,134)(117,133)(118,138)(119,137)(120,136)(145,177)(146,176)(147,175)
(148,180)(149,179)(150,178)(151,171)(152,170)(153,169)(154,174)(155,173)
(156,172)(157,183)(158,182)(159,181)(160,186)(161,185)(162,184)(163,189)
(164,188)(165,187)(166,192)(167,191)(168,190)(193,243)(194,242)(195,241)
(196,246)(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)(203,251)
(204,250)(205,261)(206,260)(207,259)(208,264)(209,263)(210,262)(211,255)
(212,254)(213,253)(214,258)(215,257)(216,256)(217,267)(218,266)(219,265)
(220,270)(221,269)(222,268)(223,273)(224,272)(225,271)(226,276)(227,275)
(228,274)(229,285)(230,284)(231,283)(232,288)(233,287)(234,286)(235,279)
(236,278)(237,277)(238,282)(239,281)(240,280)(289,378)(290,377)(291,376)
(292,375)(293,374)(294,373)(295,384)(296,383)(297,382)(298,381)(299,380)
(300,379)(301,369)(302,368)(303,367)(304,372)(305,371)(306,370)(307,363)
(308,362)(309,361)(310,366)(311,365)(312,364)(313,351)(314,350)(315,349)
(316,354)(317,353)(318,352)(319,357)(320,356)(321,355)(322,360)(323,359)
(324,358)(325,348)(326,347)(327,346)(328,345)(329,344)(330,343)(331,342)
(332,341)(333,340)(334,339)(335,338)(336,337);
s2 := 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);
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*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope