Polytope of Type {34,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,24}*1632
Also Known As : {34,24|2}. if this polytope has another name.
Group : SmallGroup(1632,320)
Rank : 3
Schlafli Type : {34,24}
Number of vertices, edges, etc : 34, 408, 24
Order of s0s1s2 : 408
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 : {34,12}*816
3-fold quotients : {34,8}*544
4-fold quotients : {34,6}*408
6-fold quotients : {34,4}*272
12-fold quotients : {34,2}*136
17-fold quotients : {2,24}*96
24-fold quotients : {17,2}*68
34-fold quotients : {2,12}*48
51-fold quotients : {2,8}*32
68-fold quotients : {2,6}*24
102-fold quotients : {2,4}*16
136-fold quotients : {2,3}*12
204-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 17)( 3, 16)( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)( 9, 10)
( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)( 26, 27)
( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)( 43, 44)
( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)( 60, 61)
( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)( 77, 78)
( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)
(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)
(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)
(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)(145,146)
(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)
(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)(179,180)
(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(196,197)
(206,221)(207,220)(208,219)(209,218)(210,217)(211,216)(212,215)(213,214)
(223,238)(224,237)(225,236)(226,235)(227,234)(228,233)(229,232)(230,231)
(240,255)(241,254)(242,253)(243,252)(244,251)(245,250)(246,249)(247,248)
(257,272)(258,271)(259,270)(260,269)(261,268)(262,267)(263,266)(264,265)
(274,289)(275,288)(276,287)(277,286)(278,285)(279,284)(280,283)(281,282)
(291,306)(292,305)(293,304)(294,303)(295,302)(296,301)(297,300)(298,299)
(308,323)(309,322)(310,321)(311,320)(312,319)(313,318)(314,317)(315,316)
(325,340)(326,339)(327,338)(328,337)(329,336)(330,335)(331,334)(332,333)
(342,357)(343,356)(344,355)(345,354)(346,353)(347,352)(348,351)(349,350)
(359,374)(360,373)(361,372)(362,371)(363,370)(364,369)(365,368)(366,367)
(376,391)(377,390)(378,389)(379,388)(380,387)(381,386)(382,385)(383,384)
(393,408)(394,407)(395,406)(396,405)(397,404)(398,403)(399,402)(400,401);;
s1 := ( 1, 2)( 3, 17)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)
( 18, 36)( 19, 35)( 20, 51)( 21, 50)( 22, 49)( 23, 48)( 24, 47)( 25, 46)
( 26, 45)( 27, 44)( 28, 43)( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 33, 38)
( 34, 37)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)
( 60, 62)( 69, 87)( 70, 86)( 71,102)( 72,101)( 73,100)( 74, 99)( 75, 98)
( 76, 97)( 77, 96)( 78, 95)( 79, 94)( 80, 93)( 81, 92)( 82, 91)( 83, 90)
( 84, 89)( 85, 88)(103,155)(104,154)(105,170)(106,169)(107,168)(108,167)
(109,166)(110,165)(111,164)(112,163)(113,162)(114,161)(115,160)(116,159)
(117,158)(118,157)(119,156)(120,189)(121,188)(122,204)(123,203)(124,202)
(125,201)(126,200)(127,199)(128,198)(129,197)(130,196)(131,195)(132,194)
(133,193)(134,192)(135,191)(136,190)(137,172)(138,171)(139,187)(140,186)
(141,185)(142,184)(143,183)(144,182)(145,181)(146,180)(147,179)(148,178)
(149,177)(150,176)(151,175)(152,174)(153,173)(205,308)(206,307)(207,323)
(208,322)(209,321)(210,320)(211,319)(212,318)(213,317)(214,316)(215,315)
(216,314)(217,313)(218,312)(219,311)(220,310)(221,309)(222,342)(223,341)
(224,357)(225,356)(226,355)(227,354)(228,353)(229,352)(230,351)(231,350)
(232,349)(233,348)(234,347)(235,346)(236,345)(237,344)(238,343)(239,325)
(240,324)(241,340)(242,339)(243,338)(244,337)(245,336)(246,335)(247,334)
(248,333)(249,332)(250,331)(251,330)(252,329)(253,328)(254,327)(255,326)
(256,359)(257,358)(258,374)(259,373)(260,372)(261,371)(262,370)(263,369)
(264,368)(265,367)(266,366)(267,365)(268,364)(269,363)(270,362)(271,361)
(272,360)(273,393)(274,392)(275,408)(276,407)(277,406)(278,405)(279,404)
(280,403)(281,402)(282,401)(283,400)(284,399)(285,398)(286,397)(287,396)
(288,395)(289,394)(290,376)(291,375)(292,391)(293,390)(294,389)(295,388)
(296,387)(297,386)(298,385)(299,384)(300,383)(301,382)(302,381)(303,380)
(304,379)(305,378)(306,377);;
s2 := ( 1,222)( 2,223)( 3,224)( 4,225)( 5,226)( 6,227)( 7,228)( 8,229)
( 9,230)( 10,231)( 11,232)( 12,233)( 13,234)( 14,235)( 15,236)( 16,237)
( 17,238)( 18,205)( 19,206)( 20,207)( 21,208)( 22,209)( 23,210)( 24,211)
( 25,212)( 26,213)( 27,214)( 28,215)( 29,216)( 30,217)( 31,218)( 32,219)
( 33,220)( 34,221)( 35,239)( 36,240)( 37,241)( 38,242)( 39,243)( 40,244)
( 41,245)( 42,246)( 43,247)( 44,248)( 45,249)( 46,250)( 47,251)( 48,252)
( 49,253)( 50,254)( 51,255)( 52,273)( 53,274)( 54,275)( 55,276)( 56,277)
( 57,278)( 58,279)( 59,280)( 60,281)( 61,282)( 62,283)( 63,284)( 64,285)
( 65,286)( 66,287)( 67,288)( 68,289)( 69,256)( 70,257)( 71,258)( 72,259)
( 73,260)( 74,261)( 75,262)( 76,263)( 77,264)( 78,265)( 79,266)( 80,267)
( 81,268)( 82,269)( 83,270)( 84,271)( 85,272)( 86,290)( 87,291)( 88,292)
( 89,293)( 90,294)( 91,295)( 92,296)( 93,297)( 94,298)( 95,299)( 96,300)
( 97,301)( 98,302)( 99,303)(100,304)(101,305)(102,306)(103,375)(104,376)
(105,377)(106,378)(107,379)(108,380)(109,381)(110,382)(111,383)(112,384)
(113,385)(114,386)(115,387)(116,388)(117,389)(118,390)(119,391)(120,358)
(121,359)(122,360)(123,361)(124,362)(125,363)(126,364)(127,365)(128,366)
(129,367)(130,368)(131,369)(132,370)(133,371)(134,372)(135,373)(136,374)
(137,392)(138,393)(139,394)(140,395)(141,396)(142,397)(143,398)(144,399)
(145,400)(146,401)(147,402)(148,403)(149,404)(150,405)(151,406)(152,407)
(153,408)(154,324)(155,325)(156,326)(157,327)(158,328)(159,329)(160,330)
(161,331)(162,332)(163,333)(164,334)(165,335)(166,336)(167,337)(168,338)
(169,339)(170,340)(171,307)(172,308)(173,309)(174,310)(175,311)(176,312)
(177,313)(178,314)(179,315)(180,316)(181,317)(182,318)(183,319)(184,320)
(185,321)(186,322)(187,323)(188,341)(189,342)(190,343)(191,344)(192,345)
(193,346)(194,347)(195,348)(196,349)(197,350)(198,351)(199,352)(200,353)
(201,354)(202,355)(203,356)(204,357);;
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,
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,
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*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(408)!( 2, 17)( 3, 16)( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)
( 9, 10)( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)
( 26, 27)( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)
( 43, 44)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)
( 60, 61)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)
( 77, 78)( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)
( 94, 95)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)
(111,112)(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)
(128,129)(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)
(145,146)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)
(162,163)(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)
(179,180)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)
(196,197)(206,221)(207,220)(208,219)(209,218)(210,217)(211,216)(212,215)
(213,214)(223,238)(224,237)(225,236)(226,235)(227,234)(228,233)(229,232)
(230,231)(240,255)(241,254)(242,253)(243,252)(244,251)(245,250)(246,249)
(247,248)(257,272)(258,271)(259,270)(260,269)(261,268)(262,267)(263,266)
(264,265)(274,289)(275,288)(276,287)(277,286)(278,285)(279,284)(280,283)
(281,282)(291,306)(292,305)(293,304)(294,303)(295,302)(296,301)(297,300)
(298,299)(308,323)(309,322)(310,321)(311,320)(312,319)(313,318)(314,317)
(315,316)(325,340)(326,339)(327,338)(328,337)(329,336)(330,335)(331,334)
(332,333)(342,357)(343,356)(344,355)(345,354)(346,353)(347,352)(348,351)
(349,350)(359,374)(360,373)(361,372)(362,371)(363,370)(364,369)(365,368)
(366,367)(376,391)(377,390)(378,389)(379,388)(380,387)(381,386)(382,385)
(383,384)(393,408)(394,407)(395,406)(396,405)(397,404)(398,403)(399,402)
(400,401);
s1 := Sym(408)!( 1, 2)( 3, 17)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)
( 9, 11)( 18, 36)( 19, 35)( 20, 51)( 21, 50)( 22, 49)( 23, 48)( 24, 47)
( 25, 46)( 26, 45)( 27, 44)( 28, 43)( 29, 42)( 30, 41)( 31, 40)( 32, 39)
( 33, 38)( 34, 37)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)
( 59, 63)( 60, 62)( 69, 87)( 70, 86)( 71,102)( 72,101)( 73,100)( 74, 99)
( 75, 98)( 76, 97)( 77, 96)( 78, 95)( 79, 94)( 80, 93)( 81, 92)( 82, 91)
( 83, 90)( 84, 89)( 85, 88)(103,155)(104,154)(105,170)(106,169)(107,168)
(108,167)(109,166)(110,165)(111,164)(112,163)(113,162)(114,161)(115,160)
(116,159)(117,158)(118,157)(119,156)(120,189)(121,188)(122,204)(123,203)
(124,202)(125,201)(126,200)(127,199)(128,198)(129,197)(130,196)(131,195)
(132,194)(133,193)(134,192)(135,191)(136,190)(137,172)(138,171)(139,187)
(140,186)(141,185)(142,184)(143,183)(144,182)(145,181)(146,180)(147,179)
(148,178)(149,177)(150,176)(151,175)(152,174)(153,173)(205,308)(206,307)
(207,323)(208,322)(209,321)(210,320)(211,319)(212,318)(213,317)(214,316)
(215,315)(216,314)(217,313)(218,312)(219,311)(220,310)(221,309)(222,342)
(223,341)(224,357)(225,356)(226,355)(227,354)(228,353)(229,352)(230,351)
(231,350)(232,349)(233,348)(234,347)(235,346)(236,345)(237,344)(238,343)
(239,325)(240,324)(241,340)(242,339)(243,338)(244,337)(245,336)(246,335)
(247,334)(248,333)(249,332)(250,331)(251,330)(252,329)(253,328)(254,327)
(255,326)(256,359)(257,358)(258,374)(259,373)(260,372)(261,371)(262,370)
(263,369)(264,368)(265,367)(266,366)(267,365)(268,364)(269,363)(270,362)
(271,361)(272,360)(273,393)(274,392)(275,408)(276,407)(277,406)(278,405)
(279,404)(280,403)(281,402)(282,401)(283,400)(284,399)(285,398)(286,397)
(287,396)(288,395)(289,394)(290,376)(291,375)(292,391)(293,390)(294,389)
(295,388)(296,387)(297,386)(298,385)(299,384)(300,383)(301,382)(302,381)
(303,380)(304,379)(305,378)(306,377);
s2 := Sym(408)!( 1,222)( 2,223)( 3,224)( 4,225)( 5,226)( 6,227)( 7,228)
( 8,229)( 9,230)( 10,231)( 11,232)( 12,233)( 13,234)( 14,235)( 15,236)
( 16,237)( 17,238)( 18,205)( 19,206)( 20,207)( 21,208)( 22,209)( 23,210)
( 24,211)( 25,212)( 26,213)( 27,214)( 28,215)( 29,216)( 30,217)( 31,218)
( 32,219)( 33,220)( 34,221)( 35,239)( 36,240)( 37,241)( 38,242)( 39,243)
( 40,244)( 41,245)( 42,246)( 43,247)( 44,248)( 45,249)( 46,250)( 47,251)
( 48,252)( 49,253)( 50,254)( 51,255)( 52,273)( 53,274)( 54,275)( 55,276)
( 56,277)( 57,278)( 58,279)( 59,280)( 60,281)( 61,282)( 62,283)( 63,284)
( 64,285)( 65,286)( 66,287)( 67,288)( 68,289)( 69,256)( 70,257)( 71,258)
( 72,259)( 73,260)( 74,261)( 75,262)( 76,263)( 77,264)( 78,265)( 79,266)
( 80,267)( 81,268)( 82,269)( 83,270)( 84,271)( 85,272)( 86,290)( 87,291)
( 88,292)( 89,293)( 90,294)( 91,295)( 92,296)( 93,297)( 94,298)( 95,299)
( 96,300)( 97,301)( 98,302)( 99,303)(100,304)(101,305)(102,306)(103,375)
(104,376)(105,377)(106,378)(107,379)(108,380)(109,381)(110,382)(111,383)
(112,384)(113,385)(114,386)(115,387)(116,388)(117,389)(118,390)(119,391)
(120,358)(121,359)(122,360)(123,361)(124,362)(125,363)(126,364)(127,365)
(128,366)(129,367)(130,368)(131,369)(132,370)(133,371)(134,372)(135,373)
(136,374)(137,392)(138,393)(139,394)(140,395)(141,396)(142,397)(143,398)
(144,399)(145,400)(146,401)(147,402)(148,403)(149,404)(150,405)(151,406)
(152,407)(153,408)(154,324)(155,325)(156,326)(157,327)(158,328)(159,329)
(160,330)(161,331)(162,332)(163,333)(164,334)(165,335)(166,336)(167,337)
(168,338)(169,339)(170,340)(171,307)(172,308)(173,309)(174,310)(175,311)
(176,312)(177,313)(178,314)(179,315)(180,316)(181,317)(182,318)(183,319)
(184,320)(185,321)(186,322)(187,323)(188,341)(189,342)(190,343)(191,344)
(192,345)(193,346)(194,347)(195,348)(196,349)(197,350)(198,351)(199,352)
(200,353)(201,354)(202,355)(203,356)(204,357);
poly := sub<Sym(408)|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,
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,
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*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