Polytope of Type {24,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6}*1728e
if this polytope has a name.
Group : SmallGroup(1728,30298)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 144, 432, 36
Order of s0s1s2 : 12
Order of s0s1s2s1 : 24
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 : {12,6}*864b
3-fold quotients : {24,6}*576e
4-fold quotients : {12,6}*432d
6-fold quotients : {12,6}*288a
8-fold quotients : {6,6}*216b
9-fold quotients : {8,6}*192b
12-fold quotients : {12,6}*144d
16-fold quotients : {6,6}*108
18-fold quotients : {8,3}*96, {4,6}*96
24-fold quotients : {6,6}*72a
36-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
72-fold quotients : {4,3}*24, {2,6}*24, {6,2}*24
144-fold quotients : {2,3}*12, {3,2}*12
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,221)( 2,222)( 3,224)( 4,223)( 5,218)( 6,217)( 7,219)( 8,220)
( 9,237)( 10,238)( 11,240)( 12,239)( 13,234)( 14,233)( 15,235)( 16,236)
( 17,229)( 18,230)( 19,232)( 20,231)( 21,226)( 22,225)( 23,227)( 24,228)
( 25,269)( 26,270)( 27,272)( 28,271)( 29,266)( 30,265)( 31,267)( 32,268)
( 33,285)( 34,286)( 35,288)( 36,287)( 37,282)( 38,281)( 39,283)( 40,284)
( 41,277)( 42,278)( 43,280)( 44,279)( 45,274)( 46,273)( 47,275)( 48,276)
( 49,245)( 50,246)( 51,248)( 52,247)( 53,242)( 54,241)( 55,243)( 56,244)
( 57,261)( 58,262)( 59,264)( 60,263)( 61,258)( 62,257)( 63,259)( 64,260)
( 65,253)( 66,254)( 67,256)( 68,255)( 69,250)( 70,249)( 71,251)( 72,252)
( 73,293)( 74,294)( 75,296)( 76,295)( 77,290)( 78,289)( 79,291)( 80,292)
( 81,309)( 82,310)( 83,312)( 84,311)( 85,306)( 86,305)( 87,307)( 88,308)
( 89,301)( 90,302)( 91,304)( 92,303)( 93,298)( 94,297)( 95,299)( 96,300)
( 97,341)( 98,342)( 99,344)(100,343)(101,338)(102,337)(103,339)(104,340)
(105,357)(106,358)(107,360)(108,359)(109,354)(110,353)(111,355)(112,356)
(113,349)(114,350)(115,352)(116,351)(117,346)(118,345)(119,347)(120,348)
(121,317)(122,318)(123,320)(124,319)(125,314)(126,313)(127,315)(128,316)
(129,333)(130,334)(131,336)(132,335)(133,330)(134,329)(135,331)(136,332)
(137,325)(138,326)(139,328)(140,327)(141,322)(142,321)(143,323)(144,324)
(145,365)(146,366)(147,368)(148,367)(149,362)(150,361)(151,363)(152,364)
(153,381)(154,382)(155,384)(156,383)(157,378)(158,377)(159,379)(160,380)
(161,373)(162,374)(163,376)(164,375)(165,370)(166,369)(167,371)(168,372)
(169,413)(170,414)(171,416)(172,415)(173,410)(174,409)(175,411)(176,412)
(177,429)(178,430)(179,432)(180,431)(181,426)(182,425)(183,427)(184,428)
(185,421)(186,422)(187,424)(188,423)(189,418)(190,417)(191,419)(192,420)
(193,389)(194,390)(195,392)(196,391)(197,386)(198,385)(199,387)(200,388)
(201,405)(202,406)(203,408)(204,407)(205,402)(206,401)(207,403)(208,404)
(209,397)(210,398)(211,400)(212,399)(213,394)(214,393)(215,395)(216,396);;
s1 := ( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 31)( 6, 32)( 7, 29)( 8, 30)
( 9, 33)( 10, 34)( 11, 36)( 12, 35)( 13, 39)( 14, 40)( 15, 37)( 16, 38)
( 17, 41)( 18, 42)( 19, 44)( 20, 43)( 21, 47)( 22, 48)( 23, 45)( 24, 46)
( 51, 52)( 53, 55)( 54, 56)( 59, 60)( 61, 63)( 62, 64)( 67, 68)( 69, 71)
( 70, 72)( 73,169)( 74,170)( 75,172)( 76,171)( 77,175)( 78,176)( 79,173)
( 80,174)( 81,177)( 82,178)( 83,180)( 84,179)( 85,183)( 86,184)( 87,181)
( 88,182)( 89,185)( 90,186)( 91,188)( 92,187)( 93,191)( 94,192)( 95,189)
( 96,190)( 97,145)( 98,146)( 99,148)(100,147)(101,151)(102,152)(103,149)
(104,150)(105,153)(106,154)(107,156)(108,155)(109,159)(110,160)(111,157)
(112,158)(113,161)(114,162)(115,164)(116,163)(117,167)(118,168)(119,165)
(120,166)(121,193)(122,194)(123,196)(124,195)(125,199)(126,200)(127,197)
(128,198)(129,201)(130,202)(131,204)(132,203)(133,207)(134,208)(135,205)
(136,206)(137,209)(138,210)(139,212)(140,211)(141,215)(142,216)(143,213)
(144,214)(217,242)(218,241)(219,243)(220,244)(221,248)(222,247)(223,246)
(224,245)(225,250)(226,249)(227,251)(228,252)(229,256)(230,255)(231,254)
(232,253)(233,258)(234,257)(235,259)(236,260)(237,264)(238,263)(239,262)
(240,261)(265,266)(269,272)(270,271)(273,274)(277,280)(278,279)(281,282)
(285,288)(286,287)(289,386)(290,385)(291,387)(292,388)(293,392)(294,391)
(295,390)(296,389)(297,394)(298,393)(299,395)(300,396)(301,400)(302,399)
(303,398)(304,397)(305,402)(306,401)(307,403)(308,404)(309,408)(310,407)
(311,406)(312,405)(313,362)(314,361)(315,363)(316,364)(317,368)(318,367)
(319,366)(320,365)(321,370)(322,369)(323,371)(324,372)(325,376)(326,375)
(327,374)(328,373)(329,378)(330,377)(331,379)(332,380)(333,384)(334,383)
(335,382)(336,381)(337,410)(338,409)(339,411)(340,412)(341,416)(342,415)
(343,414)(344,413)(345,418)(346,417)(347,419)(348,420)(349,424)(350,423)
(351,422)(352,421)(353,426)(354,425)(355,427)(356,428)(357,432)(358,431)
(359,430)(360,429);;
s2 := ( 1, 73)( 2, 74)( 3, 79)( 4, 80)( 5, 78)( 6, 77)( 7, 75)( 8, 76)
( 9, 89)( 10, 90)( 11, 95)( 12, 96)( 13, 94)( 14, 93)( 15, 91)( 16, 92)
( 17, 81)( 18, 82)( 19, 87)( 20, 88)( 21, 86)( 22, 85)( 23, 83)( 24, 84)
( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)( 32,108)
( 33, 97)( 34, 98)( 35,103)( 36,104)( 37,102)( 38,101)( 39, 99)( 40,100)
( 41,113)( 42,114)( 43,119)( 44,120)( 45,118)( 46,117)( 47,115)( 48,116)
( 49,137)( 50,138)( 51,143)( 52,144)( 53,142)( 54,141)( 55,139)( 56,140)
( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)( 64,132)
( 65,121)( 66,122)( 67,127)( 68,128)( 69,126)( 70,125)( 71,123)( 72,124)
(147,151)(148,152)(149,150)(153,161)(154,162)(155,167)(156,168)(157,166)
(158,165)(159,163)(160,164)(169,177)(170,178)(171,183)(172,184)(173,182)
(174,181)(175,179)(176,180)(187,191)(188,192)(189,190)(193,209)(194,210)
(195,215)(196,216)(197,214)(198,213)(199,211)(200,212)(203,207)(204,208)
(205,206)(217,290)(218,289)(219,296)(220,295)(221,293)(222,294)(223,292)
(224,291)(225,306)(226,305)(227,312)(228,311)(229,309)(230,310)(231,308)
(232,307)(233,298)(234,297)(235,304)(236,303)(237,301)(238,302)(239,300)
(240,299)(241,322)(242,321)(243,328)(244,327)(245,325)(246,326)(247,324)
(248,323)(249,314)(250,313)(251,320)(252,319)(253,317)(254,318)(255,316)
(256,315)(257,330)(258,329)(259,336)(260,335)(261,333)(262,334)(263,332)
(264,331)(265,354)(266,353)(267,360)(268,359)(269,357)(270,358)(271,356)
(272,355)(273,346)(274,345)(275,352)(276,351)(277,349)(278,350)(279,348)
(280,347)(281,338)(282,337)(283,344)(284,343)(285,341)(286,342)(287,340)
(288,339)(361,362)(363,368)(364,367)(369,378)(370,377)(371,384)(372,383)
(373,381)(374,382)(375,380)(376,379)(385,394)(386,393)(387,400)(388,399)
(389,397)(390,398)(391,396)(392,395)(401,402)(403,408)(404,407)(409,426)
(410,425)(411,432)(412,431)(413,429)(414,430)(415,428)(416,427)(417,418)
(419,424)(420,423);;
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*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0,
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 1,221)( 2,222)( 3,224)( 4,223)( 5,218)( 6,217)( 7,219)
( 8,220)( 9,237)( 10,238)( 11,240)( 12,239)( 13,234)( 14,233)( 15,235)
( 16,236)( 17,229)( 18,230)( 19,232)( 20,231)( 21,226)( 22,225)( 23,227)
( 24,228)( 25,269)( 26,270)( 27,272)( 28,271)( 29,266)( 30,265)( 31,267)
( 32,268)( 33,285)( 34,286)( 35,288)( 36,287)( 37,282)( 38,281)( 39,283)
( 40,284)( 41,277)( 42,278)( 43,280)( 44,279)( 45,274)( 46,273)( 47,275)
( 48,276)( 49,245)( 50,246)( 51,248)( 52,247)( 53,242)( 54,241)( 55,243)
( 56,244)( 57,261)( 58,262)( 59,264)( 60,263)( 61,258)( 62,257)( 63,259)
( 64,260)( 65,253)( 66,254)( 67,256)( 68,255)( 69,250)( 70,249)( 71,251)
( 72,252)( 73,293)( 74,294)( 75,296)( 76,295)( 77,290)( 78,289)( 79,291)
( 80,292)( 81,309)( 82,310)( 83,312)( 84,311)( 85,306)( 86,305)( 87,307)
( 88,308)( 89,301)( 90,302)( 91,304)( 92,303)( 93,298)( 94,297)( 95,299)
( 96,300)( 97,341)( 98,342)( 99,344)(100,343)(101,338)(102,337)(103,339)
(104,340)(105,357)(106,358)(107,360)(108,359)(109,354)(110,353)(111,355)
(112,356)(113,349)(114,350)(115,352)(116,351)(117,346)(118,345)(119,347)
(120,348)(121,317)(122,318)(123,320)(124,319)(125,314)(126,313)(127,315)
(128,316)(129,333)(130,334)(131,336)(132,335)(133,330)(134,329)(135,331)
(136,332)(137,325)(138,326)(139,328)(140,327)(141,322)(142,321)(143,323)
(144,324)(145,365)(146,366)(147,368)(148,367)(149,362)(150,361)(151,363)
(152,364)(153,381)(154,382)(155,384)(156,383)(157,378)(158,377)(159,379)
(160,380)(161,373)(162,374)(163,376)(164,375)(165,370)(166,369)(167,371)
(168,372)(169,413)(170,414)(171,416)(172,415)(173,410)(174,409)(175,411)
(176,412)(177,429)(178,430)(179,432)(180,431)(181,426)(182,425)(183,427)
(184,428)(185,421)(186,422)(187,424)(188,423)(189,418)(190,417)(191,419)
(192,420)(193,389)(194,390)(195,392)(196,391)(197,386)(198,385)(199,387)
(200,388)(201,405)(202,406)(203,408)(204,407)(205,402)(206,401)(207,403)
(208,404)(209,397)(210,398)(211,400)(212,399)(213,394)(214,393)(215,395)
(216,396);
s1 := Sym(432)!( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 31)( 6, 32)( 7, 29)
( 8, 30)( 9, 33)( 10, 34)( 11, 36)( 12, 35)( 13, 39)( 14, 40)( 15, 37)
( 16, 38)( 17, 41)( 18, 42)( 19, 44)( 20, 43)( 21, 47)( 22, 48)( 23, 45)
( 24, 46)( 51, 52)( 53, 55)( 54, 56)( 59, 60)( 61, 63)( 62, 64)( 67, 68)
( 69, 71)( 70, 72)( 73,169)( 74,170)( 75,172)( 76,171)( 77,175)( 78,176)
( 79,173)( 80,174)( 81,177)( 82,178)( 83,180)( 84,179)( 85,183)( 86,184)
( 87,181)( 88,182)( 89,185)( 90,186)( 91,188)( 92,187)( 93,191)( 94,192)
( 95,189)( 96,190)( 97,145)( 98,146)( 99,148)(100,147)(101,151)(102,152)
(103,149)(104,150)(105,153)(106,154)(107,156)(108,155)(109,159)(110,160)
(111,157)(112,158)(113,161)(114,162)(115,164)(116,163)(117,167)(118,168)
(119,165)(120,166)(121,193)(122,194)(123,196)(124,195)(125,199)(126,200)
(127,197)(128,198)(129,201)(130,202)(131,204)(132,203)(133,207)(134,208)
(135,205)(136,206)(137,209)(138,210)(139,212)(140,211)(141,215)(142,216)
(143,213)(144,214)(217,242)(218,241)(219,243)(220,244)(221,248)(222,247)
(223,246)(224,245)(225,250)(226,249)(227,251)(228,252)(229,256)(230,255)
(231,254)(232,253)(233,258)(234,257)(235,259)(236,260)(237,264)(238,263)
(239,262)(240,261)(265,266)(269,272)(270,271)(273,274)(277,280)(278,279)
(281,282)(285,288)(286,287)(289,386)(290,385)(291,387)(292,388)(293,392)
(294,391)(295,390)(296,389)(297,394)(298,393)(299,395)(300,396)(301,400)
(302,399)(303,398)(304,397)(305,402)(306,401)(307,403)(308,404)(309,408)
(310,407)(311,406)(312,405)(313,362)(314,361)(315,363)(316,364)(317,368)
(318,367)(319,366)(320,365)(321,370)(322,369)(323,371)(324,372)(325,376)
(326,375)(327,374)(328,373)(329,378)(330,377)(331,379)(332,380)(333,384)
(334,383)(335,382)(336,381)(337,410)(338,409)(339,411)(340,412)(341,416)
(342,415)(343,414)(344,413)(345,418)(346,417)(347,419)(348,420)(349,424)
(350,423)(351,422)(352,421)(353,426)(354,425)(355,427)(356,428)(357,432)
(358,431)(359,430)(360,429);
s2 := Sym(432)!( 1, 73)( 2, 74)( 3, 79)( 4, 80)( 5, 78)( 6, 77)( 7, 75)
( 8, 76)( 9, 89)( 10, 90)( 11, 95)( 12, 96)( 13, 94)( 14, 93)( 15, 91)
( 16, 92)( 17, 81)( 18, 82)( 19, 87)( 20, 88)( 21, 86)( 22, 85)( 23, 83)
( 24, 84)( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)
( 32,108)( 33, 97)( 34, 98)( 35,103)( 36,104)( 37,102)( 38,101)( 39, 99)
( 40,100)( 41,113)( 42,114)( 43,119)( 44,120)( 45,118)( 46,117)( 47,115)
( 48,116)( 49,137)( 50,138)( 51,143)( 52,144)( 53,142)( 54,141)( 55,139)
( 56,140)( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)
( 64,132)( 65,121)( 66,122)( 67,127)( 68,128)( 69,126)( 70,125)( 71,123)
( 72,124)(147,151)(148,152)(149,150)(153,161)(154,162)(155,167)(156,168)
(157,166)(158,165)(159,163)(160,164)(169,177)(170,178)(171,183)(172,184)
(173,182)(174,181)(175,179)(176,180)(187,191)(188,192)(189,190)(193,209)
(194,210)(195,215)(196,216)(197,214)(198,213)(199,211)(200,212)(203,207)
(204,208)(205,206)(217,290)(218,289)(219,296)(220,295)(221,293)(222,294)
(223,292)(224,291)(225,306)(226,305)(227,312)(228,311)(229,309)(230,310)
(231,308)(232,307)(233,298)(234,297)(235,304)(236,303)(237,301)(238,302)
(239,300)(240,299)(241,322)(242,321)(243,328)(244,327)(245,325)(246,326)
(247,324)(248,323)(249,314)(250,313)(251,320)(252,319)(253,317)(254,318)
(255,316)(256,315)(257,330)(258,329)(259,336)(260,335)(261,333)(262,334)
(263,332)(264,331)(265,354)(266,353)(267,360)(268,359)(269,357)(270,358)
(271,356)(272,355)(273,346)(274,345)(275,352)(276,351)(277,349)(278,350)
(279,348)(280,347)(281,338)(282,337)(283,344)(284,343)(285,341)(286,342)
(287,340)(288,339)(361,362)(363,368)(364,367)(369,378)(370,377)(371,384)
(372,383)(373,381)(374,382)(375,380)(376,379)(385,394)(386,393)(387,400)
(388,399)(389,397)(390,398)(391,396)(392,395)(401,402)(403,408)(404,407)
(409,426)(410,425)(411,432)(412,431)(413,429)(414,430)(415,428)(416,427)
(417,418)(419,424)(420,423);
poly := sub<Sym(432)|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*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0,
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope