Polytope of Type {24,36}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,36}*1728c
Also Known As : {24,36|2}. if this polytope has another name.
Group : SmallGroup(1728,4743)
Rank : 3
Schlafli Type : {24,36}
Number of vertices, edges, etc : 24, 432, 36
Order of s0s1s2 : 72
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {24,18}*864a, {12,36}*864a
3-fold quotients : {8,36}*576a, {24,12}*576c
4-fold quotients : {6,36}*432a, {12,18}*432a
6-fold quotients : {4,36}*288a, {8,18}*288, {24,6}*288a, {12,12}*288a
8-fold quotients : {6,18}*216a
9-fold quotients : {24,4}*192a, {8,12}*192a
12-fold quotients : {2,36}*144, {4,18}*144a, {6,12}*144a, {12,6}*144a
18-fold quotients : {4,12}*96a, {12,4}*96a, {24,2}*96, {8,6}*96
24-fold quotients : {2,18}*72, {6,6}*72a
27-fold quotients : {8,4}*64a
36-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
48-fold quotients : {2,9}*36
54-fold quotients : {4,4}*32, {8,2}*32
72-fold quotients : {2,6}*24, {6,2}*24
108-fold quotients : {2,4}*16, {4,2}*16
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 := ( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)
( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)
( 50, 53)( 51, 54)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)
( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)
( 96, 99)(103,106)(104,107)(105,108)(109,136)(110,137)(111,138)(112,142)
(113,143)(114,144)(115,139)(116,140)(117,141)(118,145)(119,146)(120,147)
(121,151)(122,152)(123,153)(124,148)(125,149)(126,150)(127,154)(128,155)
(129,156)(130,160)(131,161)(132,162)(133,157)(134,158)(135,159)(163,190)
(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)(170,194)(171,195)
(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)(179,203)
(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)(186,216)(187,211)
(188,212)(189,213)(217,325)(218,326)(219,327)(220,331)(221,332)(222,333)
(223,328)(224,329)(225,330)(226,334)(227,335)(228,336)(229,340)(230,341)
(231,342)(232,337)(233,338)(234,339)(235,343)(236,344)(237,345)(238,349)
(239,350)(240,351)(241,346)(242,347)(243,348)(244,352)(245,353)(246,354)
(247,358)(248,359)(249,360)(250,355)(251,356)(252,357)(253,361)(254,362)
(255,363)(256,367)(257,368)(258,369)(259,364)(260,365)(261,366)(262,370)
(263,371)(264,372)(265,376)(266,377)(267,378)(268,373)(269,374)(270,375)
(271,379)(272,380)(273,381)(274,385)(275,386)(276,387)(277,382)(278,383)
(279,384)(280,388)(281,389)(282,390)(283,394)(284,395)(285,396)(286,391)
(287,392)(288,393)(289,397)(290,398)(291,399)(292,403)(293,404)(294,405)
(295,400)(296,401)(297,402)(298,406)(299,407)(300,408)(301,412)(302,413)
(303,414)(304,409)(305,410)(306,411)(307,415)(308,416)(309,417)(310,421)
(311,422)(312,423)(313,418)(314,419)(315,420)(316,424)(317,425)(318,426)
(319,430)(320,431)(321,432)(322,427)(323,428)(324,429);;
s1 := ( 1,220)( 2,222)( 3,221)( 4,217)( 5,219)( 6,218)( 7,223)( 8,225)
( 9,224)( 10,240)( 11,239)( 12,238)( 13,237)( 14,236)( 15,235)( 16,243)
( 17,242)( 18,241)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)( 24,226)
( 25,234)( 26,233)( 27,232)( 28,247)( 29,249)( 30,248)( 31,244)( 32,246)
( 33,245)( 34,250)( 35,252)( 36,251)( 37,267)( 38,266)( 39,265)( 40,264)
( 41,263)( 42,262)( 43,270)( 44,269)( 45,268)( 46,258)( 47,257)( 48,256)
( 49,255)( 50,254)( 51,253)( 52,261)( 53,260)( 54,259)( 55,274)( 56,276)
( 57,275)( 58,271)( 59,273)( 60,272)( 61,277)( 62,279)( 63,278)( 64,294)
( 65,293)( 66,292)( 67,291)( 68,290)( 69,289)( 70,297)( 71,296)( 72,295)
( 73,285)( 74,284)( 75,283)( 76,282)( 77,281)( 78,280)( 79,288)( 80,287)
( 81,286)( 82,301)( 83,303)( 84,302)( 85,298)( 86,300)( 87,299)( 88,304)
( 89,306)( 90,305)( 91,321)( 92,320)( 93,319)( 94,318)( 95,317)( 96,316)
( 97,324)( 98,323)( 99,322)(100,312)(101,311)(102,310)(103,309)(104,308)
(105,307)(106,315)(107,314)(108,313)(109,355)(110,357)(111,356)(112,352)
(113,354)(114,353)(115,358)(116,360)(117,359)(118,375)(119,374)(120,373)
(121,372)(122,371)(123,370)(124,378)(125,377)(126,376)(127,366)(128,365)
(129,364)(130,363)(131,362)(132,361)(133,369)(134,368)(135,367)(136,328)
(137,330)(138,329)(139,325)(140,327)(141,326)(142,331)(143,333)(144,332)
(145,348)(146,347)(147,346)(148,345)(149,344)(150,343)(151,351)(152,350)
(153,349)(154,339)(155,338)(156,337)(157,336)(158,335)(159,334)(160,342)
(161,341)(162,340)(163,409)(164,411)(165,410)(166,406)(167,408)(168,407)
(169,412)(170,414)(171,413)(172,429)(173,428)(174,427)(175,426)(176,425)
(177,424)(178,432)(179,431)(180,430)(181,420)(182,419)(183,418)(184,417)
(185,416)(186,415)(187,423)(188,422)(189,421)(190,382)(191,384)(192,383)
(193,379)(194,381)(195,380)(196,385)(197,387)(198,386)(199,402)(200,401)
(201,400)(202,399)(203,398)(204,397)(205,405)(206,404)(207,403)(208,393)
(209,392)(210,391)(211,390)(212,389)(213,388)(214,396)(215,395)(216,394);;
s2 := ( 1, 10)( 2, 12)( 3, 11)( 4, 13)( 5, 15)( 6, 14)( 7, 16)( 8, 18)
( 9, 17)( 19, 21)( 22, 24)( 25, 27)( 28, 37)( 29, 39)( 30, 38)( 31, 40)
( 32, 42)( 33, 41)( 34, 43)( 35, 45)( 36, 44)( 46, 48)( 49, 51)( 52, 54)
( 55, 64)( 56, 66)( 57, 65)( 58, 67)( 59, 69)( 60, 68)( 61, 70)( 62, 72)
( 63, 71)( 73, 75)( 76, 78)( 79, 81)( 82, 91)( 83, 93)( 84, 92)( 85, 94)
( 86, 96)( 87, 95)( 88, 97)( 89, 99)( 90, 98)(100,102)(103,105)(106,108)
(109,118)(110,120)(111,119)(112,121)(113,123)(114,122)(115,124)(116,126)
(117,125)(127,129)(130,132)(133,135)(136,145)(137,147)(138,146)(139,148)
(140,150)(141,149)(142,151)(143,153)(144,152)(154,156)(157,159)(160,162)
(163,172)(164,174)(165,173)(166,175)(167,177)(168,176)(169,178)(170,180)
(171,179)(181,183)(184,186)(187,189)(190,199)(191,201)(192,200)(193,202)
(194,204)(195,203)(196,205)(197,207)(198,206)(208,210)(211,213)(214,216)
(217,280)(218,282)(219,281)(220,283)(221,285)(222,284)(223,286)(224,288)
(225,287)(226,271)(227,273)(228,272)(229,274)(230,276)(231,275)(232,277)
(233,279)(234,278)(235,291)(236,290)(237,289)(238,294)(239,293)(240,292)
(241,297)(242,296)(243,295)(244,307)(245,309)(246,308)(247,310)(248,312)
(249,311)(250,313)(251,315)(252,314)(253,298)(254,300)(255,299)(256,301)
(257,303)(258,302)(259,304)(260,306)(261,305)(262,318)(263,317)(264,316)
(265,321)(266,320)(267,319)(268,324)(269,323)(270,322)(325,388)(326,390)
(327,389)(328,391)(329,393)(330,392)(331,394)(332,396)(333,395)(334,379)
(335,381)(336,380)(337,382)(338,384)(339,383)(340,385)(341,387)(342,386)
(343,399)(344,398)(345,397)(346,402)(347,401)(348,400)(349,405)(350,404)
(351,403)(352,415)(353,417)(354,416)(355,418)(356,420)(357,419)(358,421)
(359,423)(360,422)(361,406)(362,408)(363,407)(364,409)(365,411)(366,410)
(367,412)(368,414)(369,413)(370,426)(371,425)(372,424)(373,429)(374,428)
(375,427)(376,432)(377,431)(378,430);;
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, s0*s1*s2*s1*s0*s1*s2*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*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)
( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)
( 49, 52)( 50, 53)( 51, 54)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)
( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)
( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(109,136)(110,137)(111,138)
(112,142)(113,143)(114,144)(115,139)(116,140)(117,141)(118,145)(119,146)
(120,147)(121,151)(122,152)(123,153)(124,148)(125,149)(126,150)(127,154)
(128,155)(129,156)(130,160)(131,161)(132,162)(133,157)(134,158)(135,159)
(163,190)(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)(170,194)
(171,195)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)
(179,203)(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)(186,216)
(187,211)(188,212)(189,213)(217,325)(218,326)(219,327)(220,331)(221,332)
(222,333)(223,328)(224,329)(225,330)(226,334)(227,335)(228,336)(229,340)
(230,341)(231,342)(232,337)(233,338)(234,339)(235,343)(236,344)(237,345)
(238,349)(239,350)(240,351)(241,346)(242,347)(243,348)(244,352)(245,353)
(246,354)(247,358)(248,359)(249,360)(250,355)(251,356)(252,357)(253,361)
(254,362)(255,363)(256,367)(257,368)(258,369)(259,364)(260,365)(261,366)
(262,370)(263,371)(264,372)(265,376)(266,377)(267,378)(268,373)(269,374)
(270,375)(271,379)(272,380)(273,381)(274,385)(275,386)(276,387)(277,382)
(278,383)(279,384)(280,388)(281,389)(282,390)(283,394)(284,395)(285,396)
(286,391)(287,392)(288,393)(289,397)(290,398)(291,399)(292,403)(293,404)
(294,405)(295,400)(296,401)(297,402)(298,406)(299,407)(300,408)(301,412)
(302,413)(303,414)(304,409)(305,410)(306,411)(307,415)(308,416)(309,417)
(310,421)(311,422)(312,423)(313,418)(314,419)(315,420)(316,424)(317,425)
(318,426)(319,430)(320,431)(321,432)(322,427)(323,428)(324,429);
s1 := Sym(432)!( 1,220)( 2,222)( 3,221)( 4,217)( 5,219)( 6,218)( 7,223)
( 8,225)( 9,224)( 10,240)( 11,239)( 12,238)( 13,237)( 14,236)( 15,235)
( 16,243)( 17,242)( 18,241)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)
( 24,226)( 25,234)( 26,233)( 27,232)( 28,247)( 29,249)( 30,248)( 31,244)
( 32,246)( 33,245)( 34,250)( 35,252)( 36,251)( 37,267)( 38,266)( 39,265)
( 40,264)( 41,263)( 42,262)( 43,270)( 44,269)( 45,268)( 46,258)( 47,257)
( 48,256)( 49,255)( 50,254)( 51,253)( 52,261)( 53,260)( 54,259)( 55,274)
( 56,276)( 57,275)( 58,271)( 59,273)( 60,272)( 61,277)( 62,279)( 63,278)
( 64,294)( 65,293)( 66,292)( 67,291)( 68,290)( 69,289)( 70,297)( 71,296)
( 72,295)( 73,285)( 74,284)( 75,283)( 76,282)( 77,281)( 78,280)( 79,288)
( 80,287)( 81,286)( 82,301)( 83,303)( 84,302)( 85,298)( 86,300)( 87,299)
( 88,304)( 89,306)( 90,305)( 91,321)( 92,320)( 93,319)( 94,318)( 95,317)
( 96,316)( 97,324)( 98,323)( 99,322)(100,312)(101,311)(102,310)(103,309)
(104,308)(105,307)(106,315)(107,314)(108,313)(109,355)(110,357)(111,356)
(112,352)(113,354)(114,353)(115,358)(116,360)(117,359)(118,375)(119,374)
(120,373)(121,372)(122,371)(123,370)(124,378)(125,377)(126,376)(127,366)
(128,365)(129,364)(130,363)(131,362)(132,361)(133,369)(134,368)(135,367)
(136,328)(137,330)(138,329)(139,325)(140,327)(141,326)(142,331)(143,333)
(144,332)(145,348)(146,347)(147,346)(148,345)(149,344)(150,343)(151,351)
(152,350)(153,349)(154,339)(155,338)(156,337)(157,336)(158,335)(159,334)
(160,342)(161,341)(162,340)(163,409)(164,411)(165,410)(166,406)(167,408)
(168,407)(169,412)(170,414)(171,413)(172,429)(173,428)(174,427)(175,426)
(176,425)(177,424)(178,432)(179,431)(180,430)(181,420)(182,419)(183,418)
(184,417)(185,416)(186,415)(187,423)(188,422)(189,421)(190,382)(191,384)
(192,383)(193,379)(194,381)(195,380)(196,385)(197,387)(198,386)(199,402)
(200,401)(201,400)(202,399)(203,398)(204,397)(205,405)(206,404)(207,403)
(208,393)(209,392)(210,391)(211,390)(212,389)(213,388)(214,396)(215,395)
(216,394);
s2 := Sym(432)!( 1, 10)( 2, 12)( 3, 11)( 4, 13)( 5, 15)( 6, 14)( 7, 16)
( 8, 18)( 9, 17)( 19, 21)( 22, 24)( 25, 27)( 28, 37)( 29, 39)( 30, 38)
( 31, 40)( 32, 42)( 33, 41)( 34, 43)( 35, 45)( 36, 44)( 46, 48)( 49, 51)
( 52, 54)( 55, 64)( 56, 66)( 57, 65)( 58, 67)( 59, 69)( 60, 68)( 61, 70)
( 62, 72)( 63, 71)( 73, 75)( 76, 78)( 79, 81)( 82, 91)( 83, 93)( 84, 92)
( 85, 94)( 86, 96)( 87, 95)( 88, 97)( 89, 99)( 90, 98)(100,102)(103,105)
(106,108)(109,118)(110,120)(111,119)(112,121)(113,123)(114,122)(115,124)
(116,126)(117,125)(127,129)(130,132)(133,135)(136,145)(137,147)(138,146)
(139,148)(140,150)(141,149)(142,151)(143,153)(144,152)(154,156)(157,159)
(160,162)(163,172)(164,174)(165,173)(166,175)(167,177)(168,176)(169,178)
(170,180)(171,179)(181,183)(184,186)(187,189)(190,199)(191,201)(192,200)
(193,202)(194,204)(195,203)(196,205)(197,207)(198,206)(208,210)(211,213)
(214,216)(217,280)(218,282)(219,281)(220,283)(221,285)(222,284)(223,286)
(224,288)(225,287)(226,271)(227,273)(228,272)(229,274)(230,276)(231,275)
(232,277)(233,279)(234,278)(235,291)(236,290)(237,289)(238,294)(239,293)
(240,292)(241,297)(242,296)(243,295)(244,307)(245,309)(246,308)(247,310)
(248,312)(249,311)(250,313)(251,315)(252,314)(253,298)(254,300)(255,299)
(256,301)(257,303)(258,302)(259,304)(260,306)(261,305)(262,318)(263,317)
(264,316)(265,321)(266,320)(267,319)(268,324)(269,323)(270,322)(325,388)
(326,390)(327,389)(328,391)(329,393)(330,392)(331,394)(332,396)(333,395)
(334,379)(335,381)(336,380)(337,382)(338,384)(339,383)(340,385)(341,387)
(342,386)(343,399)(344,398)(345,397)(346,402)(347,401)(348,400)(349,405)
(350,404)(351,403)(352,415)(353,417)(354,416)(355,418)(356,420)(357,419)
(358,421)(359,423)(360,422)(361,406)(362,408)(363,407)(364,409)(365,411)
(366,410)(367,412)(368,414)(369,413)(370,426)(371,425)(372,424)(373,429)
(374,428)(375,427)(376,432)(377,431)(378,430);
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, s0*s1*s2*s1*s0*s1*s2*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*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope