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Polytope of Type {34,4,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,4,3}*1632
Also Known As : {{34,4|2},{4,3}}. if this polytope has another name.
Group : SmallGroup(1632,1195)
Rank : 4
Schlafli Type : {34,4,3}
Number of vertices, edges, etc : 34, 136, 12, 6
Order of s0s1s2s3 : 102
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   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) :
   4-fold quotients : {34,2,3}*408
   8-fold quotients : {17,2,3}*204
   17-fold quotients : {2,4,3}*96
   34-fold quotients : {2,4,3}*48
   68-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  5, 65)(  6, 66)(  7, 67)(  8, 68)(  9, 61)( 10, 62)( 11, 63)( 12, 64)
( 13, 57)( 14, 58)( 15, 59)( 16, 60)( 17, 53)( 18, 54)( 19, 55)( 20, 56)
( 21, 49)( 22, 50)( 23, 51)( 24, 52)( 25, 45)( 26, 46)( 27, 47)( 28, 48)
( 29, 41)( 30, 42)( 31, 43)( 32, 44)( 33, 37)( 34, 38)( 35, 39)( 36, 40)
( 73,133)( 74,134)( 75,135)( 76,136)( 77,129)( 78,130)( 79,131)( 80,132)
( 81,125)( 82,126)( 83,127)( 84,128)( 85,121)( 86,122)( 87,123)( 88,124)
( 89,117)( 90,118)( 91,119)( 92,120)( 93,113)( 94,114)( 95,115)( 96,116)
( 97,109)( 98,110)( 99,111)(100,112)(101,105)(102,106)(103,107)(104,108)
(141,201)(142,202)(143,203)(144,204)(145,197)(146,198)(147,199)(148,200)
(149,193)(150,194)(151,195)(152,196)(153,189)(154,190)(155,191)(156,192)
(157,185)(158,186)(159,187)(160,188)(161,181)(162,182)(163,183)(164,184)
(165,177)(166,178)(167,179)(168,180)(169,173)(170,174)(171,175)(172,176)
(209,269)(210,270)(211,271)(212,272)(213,265)(214,266)(215,267)(216,268)
(217,261)(218,262)(219,263)(220,264)(221,257)(222,258)(223,259)(224,260)
(225,253)(226,254)(227,255)(228,256)(229,249)(230,250)(231,251)(232,252)
(233,245)(234,246)(235,247)(236,248)(237,241)(238,242)(239,243)(240,244)
(277,337)(278,338)(279,339)(280,340)(281,333)(282,334)(283,335)(284,336)
(285,329)(286,330)(287,331)(288,332)(289,325)(290,326)(291,327)(292,328)
(293,321)(294,322)(295,323)(296,324)(297,317)(298,318)(299,319)(300,320)
(301,313)(302,314)(303,315)(304,316)(305,309)(306,310)(307,311)(308,312)
(345,405)(346,406)(347,407)(348,408)(349,401)(350,402)(351,403)(352,404)
(353,397)(354,398)(355,399)(356,400)(357,393)(358,394)(359,395)(360,396)
(361,389)(362,390)(363,391)(364,392)(365,385)(366,386)(367,387)(368,388)
(369,381)(370,382)(371,383)(372,384)(373,377)(374,378)(375,379)(376,380);;
s1 := (  1,211)(  2,212)(  3,209)(  4,210)(  5,207)(  6,208)(  7,205)(  8,206)
(  9,271)( 10,272)( 11,269)( 12,270)( 13,267)( 14,268)( 15,265)( 16,266)
( 17,263)( 18,264)( 19,261)( 20,262)( 21,259)( 22,260)( 23,257)( 24,258)
( 25,255)( 26,256)( 27,253)( 28,254)( 29,251)( 30,252)( 31,249)( 32,250)
( 33,247)( 34,248)( 35,245)( 36,246)( 37,243)( 38,244)( 39,241)( 40,242)
( 41,239)( 42,240)( 43,237)( 44,238)( 45,235)( 46,236)( 47,233)( 48,234)
( 49,231)( 50,232)( 51,229)( 52,230)( 53,227)( 54,228)( 55,225)( 56,226)
( 57,223)( 58,224)( 59,221)( 60,222)( 61,219)( 62,220)( 63,217)( 64,218)
( 65,215)( 66,216)( 67,213)( 68,214)( 69,279)( 70,280)( 71,277)( 72,278)
( 73,275)( 74,276)( 75,273)( 76,274)( 77,339)( 78,340)( 79,337)( 80,338)
( 81,335)( 82,336)( 83,333)( 84,334)( 85,331)( 86,332)( 87,329)( 88,330)
( 89,327)( 90,328)( 91,325)( 92,326)( 93,323)( 94,324)( 95,321)( 96,322)
( 97,319)( 98,320)( 99,317)(100,318)(101,315)(102,316)(103,313)(104,314)
(105,311)(106,312)(107,309)(108,310)(109,307)(110,308)(111,305)(112,306)
(113,303)(114,304)(115,301)(116,302)(117,299)(118,300)(119,297)(120,298)
(121,295)(122,296)(123,293)(124,294)(125,291)(126,292)(127,289)(128,290)
(129,287)(130,288)(131,285)(132,286)(133,283)(134,284)(135,281)(136,282)
(137,347)(138,348)(139,345)(140,346)(141,343)(142,344)(143,341)(144,342)
(145,407)(146,408)(147,405)(148,406)(149,403)(150,404)(151,401)(152,402)
(153,399)(154,400)(155,397)(156,398)(157,395)(158,396)(159,393)(160,394)
(161,391)(162,392)(163,389)(164,390)(165,387)(166,388)(167,385)(168,386)
(169,383)(170,384)(171,381)(172,382)(173,379)(174,380)(175,377)(176,378)
(177,375)(178,376)(179,373)(180,374)(181,371)(182,372)(183,369)(184,370)
(185,367)(186,368)(187,365)(188,366)(189,363)(190,364)(191,361)(192,362)
(193,359)(194,360)(195,357)(196,358)(197,355)(198,356)(199,353)(200,354)
(201,351)(202,352)(203,349)(204,350);;
s2 := (  3,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)
( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 59, 60)( 63, 64)
( 67, 68)( 69,137)( 70,138)( 71,140)( 72,139)( 73,141)( 74,142)( 75,144)
( 76,143)( 77,145)( 78,146)( 79,148)( 80,147)( 81,149)( 82,150)( 83,152)
( 84,151)( 85,153)( 86,154)( 87,156)( 88,155)( 89,157)( 90,158)( 91,160)
( 92,159)( 93,161)( 94,162)( 95,164)( 96,163)( 97,165)( 98,166)( 99,168)
(100,167)(101,169)(102,170)(103,172)(104,171)(105,173)(106,174)(107,176)
(108,175)(109,177)(110,178)(111,180)(112,179)(113,181)(114,182)(115,184)
(116,183)(117,185)(118,186)(119,188)(120,187)(121,189)(122,190)(123,192)
(124,191)(125,193)(126,194)(127,196)(128,195)(129,197)(130,198)(131,200)
(132,199)(133,201)(134,202)(135,204)(136,203)(207,208)(211,212)(215,216)
(219,220)(223,224)(227,228)(231,232)(235,236)(239,240)(243,244)(247,248)
(251,252)(255,256)(259,260)(263,264)(267,268)(271,272)(273,341)(274,342)
(275,344)(276,343)(277,345)(278,346)(279,348)(280,347)(281,349)(282,350)
(283,352)(284,351)(285,353)(286,354)(287,356)(288,355)(289,357)(290,358)
(291,360)(292,359)(293,361)(294,362)(295,364)(296,363)(297,365)(298,366)
(299,368)(300,367)(301,369)(302,370)(303,372)(304,371)(305,373)(306,374)
(307,376)(308,375)(309,377)(310,378)(311,380)(312,379)(313,381)(314,382)
(315,384)(316,383)(317,385)(318,386)(319,388)(320,387)(321,389)(322,390)
(323,392)(324,391)(325,393)(326,394)(327,396)(328,395)(329,397)(330,398)
(331,400)(332,399)(333,401)(334,402)(335,404)(336,403)(337,405)(338,406)
(339,408)(340,407);;
s3 := (  1, 69)(  2, 72)(  3, 71)(  4, 70)(  5, 73)(  6, 76)(  7, 75)(  8, 74)
(  9, 77)( 10, 80)( 11, 79)( 12, 78)( 13, 81)( 14, 84)( 15, 83)( 16, 82)
( 17, 85)( 18, 88)( 19, 87)( 20, 86)( 21, 89)( 22, 92)( 23, 91)( 24, 90)
( 25, 93)( 26, 96)( 27, 95)( 28, 94)( 29, 97)( 30,100)( 31, 99)( 32, 98)
( 33,101)( 34,104)( 35,103)( 36,102)( 37,105)( 38,108)( 39,107)( 40,106)
( 41,109)( 42,112)( 43,111)( 44,110)( 45,113)( 46,116)( 47,115)( 48,114)
( 49,117)( 50,120)( 51,119)( 52,118)( 53,121)( 54,124)( 55,123)( 56,122)
( 57,125)( 58,128)( 59,127)( 60,126)( 61,129)( 62,132)( 63,131)( 64,130)
( 65,133)( 66,136)( 67,135)( 68,134)(138,140)(142,144)(146,148)(150,152)
(154,156)(158,160)(162,164)(166,168)(170,172)(174,176)(178,180)(182,184)
(186,188)(190,192)(194,196)(198,200)(202,204)(205,273)(206,276)(207,275)
(208,274)(209,277)(210,280)(211,279)(212,278)(213,281)(214,284)(215,283)
(216,282)(217,285)(218,288)(219,287)(220,286)(221,289)(222,292)(223,291)
(224,290)(225,293)(226,296)(227,295)(228,294)(229,297)(230,300)(231,299)
(232,298)(233,301)(234,304)(235,303)(236,302)(237,305)(238,308)(239,307)
(240,306)(241,309)(242,312)(243,311)(244,310)(245,313)(246,316)(247,315)
(248,314)(249,317)(250,320)(251,319)(252,318)(253,321)(254,324)(255,323)
(256,322)(257,325)(258,328)(259,327)(260,326)(261,329)(262,332)(263,331)
(264,330)(265,333)(266,336)(267,335)(268,334)(269,337)(270,340)(271,339)
(272,338)(342,344)(346,348)(350,352)(354,356)(358,360)(362,364)(366,368)
(370,372)(374,376)(378,380)(382,384)(386,388)(390,392)(394,396)(398,400)
(402,404)(406,408);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, 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)!(  5, 65)(  6, 66)(  7, 67)(  8, 68)(  9, 61)( 10, 62)( 11, 63)
( 12, 64)( 13, 57)( 14, 58)( 15, 59)( 16, 60)( 17, 53)( 18, 54)( 19, 55)
( 20, 56)( 21, 49)( 22, 50)( 23, 51)( 24, 52)( 25, 45)( 26, 46)( 27, 47)
( 28, 48)( 29, 41)( 30, 42)( 31, 43)( 32, 44)( 33, 37)( 34, 38)( 35, 39)
( 36, 40)( 73,133)( 74,134)( 75,135)( 76,136)( 77,129)( 78,130)( 79,131)
( 80,132)( 81,125)( 82,126)( 83,127)( 84,128)( 85,121)( 86,122)( 87,123)
( 88,124)( 89,117)( 90,118)( 91,119)( 92,120)( 93,113)( 94,114)( 95,115)
( 96,116)( 97,109)( 98,110)( 99,111)(100,112)(101,105)(102,106)(103,107)
(104,108)(141,201)(142,202)(143,203)(144,204)(145,197)(146,198)(147,199)
(148,200)(149,193)(150,194)(151,195)(152,196)(153,189)(154,190)(155,191)
(156,192)(157,185)(158,186)(159,187)(160,188)(161,181)(162,182)(163,183)
(164,184)(165,177)(166,178)(167,179)(168,180)(169,173)(170,174)(171,175)
(172,176)(209,269)(210,270)(211,271)(212,272)(213,265)(214,266)(215,267)
(216,268)(217,261)(218,262)(219,263)(220,264)(221,257)(222,258)(223,259)
(224,260)(225,253)(226,254)(227,255)(228,256)(229,249)(230,250)(231,251)
(232,252)(233,245)(234,246)(235,247)(236,248)(237,241)(238,242)(239,243)
(240,244)(277,337)(278,338)(279,339)(280,340)(281,333)(282,334)(283,335)
(284,336)(285,329)(286,330)(287,331)(288,332)(289,325)(290,326)(291,327)
(292,328)(293,321)(294,322)(295,323)(296,324)(297,317)(298,318)(299,319)
(300,320)(301,313)(302,314)(303,315)(304,316)(305,309)(306,310)(307,311)
(308,312)(345,405)(346,406)(347,407)(348,408)(349,401)(350,402)(351,403)
(352,404)(353,397)(354,398)(355,399)(356,400)(357,393)(358,394)(359,395)
(360,396)(361,389)(362,390)(363,391)(364,392)(365,385)(366,386)(367,387)
(368,388)(369,381)(370,382)(371,383)(372,384)(373,377)(374,378)(375,379)
(376,380);
s1 := Sym(408)!(  1,211)(  2,212)(  3,209)(  4,210)(  5,207)(  6,208)(  7,205)
(  8,206)(  9,271)( 10,272)( 11,269)( 12,270)( 13,267)( 14,268)( 15,265)
( 16,266)( 17,263)( 18,264)( 19,261)( 20,262)( 21,259)( 22,260)( 23,257)
( 24,258)( 25,255)( 26,256)( 27,253)( 28,254)( 29,251)( 30,252)( 31,249)
( 32,250)( 33,247)( 34,248)( 35,245)( 36,246)( 37,243)( 38,244)( 39,241)
( 40,242)( 41,239)( 42,240)( 43,237)( 44,238)( 45,235)( 46,236)( 47,233)
( 48,234)( 49,231)( 50,232)( 51,229)( 52,230)( 53,227)( 54,228)( 55,225)
( 56,226)( 57,223)( 58,224)( 59,221)( 60,222)( 61,219)( 62,220)( 63,217)
( 64,218)( 65,215)( 66,216)( 67,213)( 68,214)( 69,279)( 70,280)( 71,277)
( 72,278)( 73,275)( 74,276)( 75,273)( 76,274)( 77,339)( 78,340)( 79,337)
( 80,338)( 81,335)( 82,336)( 83,333)( 84,334)( 85,331)( 86,332)( 87,329)
( 88,330)( 89,327)( 90,328)( 91,325)( 92,326)( 93,323)( 94,324)( 95,321)
( 96,322)( 97,319)( 98,320)( 99,317)(100,318)(101,315)(102,316)(103,313)
(104,314)(105,311)(106,312)(107,309)(108,310)(109,307)(110,308)(111,305)
(112,306)(113,303)(114,304)(115,301)(116,302)(117,299)(118,300)(119,297)
(120,298)(121,295)(122,296)(123,293)(124,294)(125,291)(126,292)(127,289)
(128,290)(129,287)(130,288)(131,285)(132,286)(133,283)(134,284)(135,281)
(136,282)(137,347)(138,348)(139,345)(140,346)(141,343)(142,344)(143,341)
(144,342)(145,407)(146,408)(147,405)(148,406)(149,403)(150,404)(151,401)
(152,402)(153,399)(154,400)(155,397)(156,398)(157,395)(158,396)(159,393)
(160,394)(161,391)(162,392)(163,389)(164,390)(165,387)(166,388)(167,385)
(168,386)(169,383)(170,384)(171,381)(172,382)(173,379)(174,380)(175,377)
(176,378)(177,375)(178,376)(179,373)(180,374)(181,371)(182,372)(183,369)
(184,370)(185,367)(186,368)(187,365)(188,366)(189,363)(190,364)(191,361)
(192,362)(193,359)(194,360)(195,357)(196,358)(197,355)(198,356)(199,353)
(200,354)(201,351)(202,352)(203,349)(204,350);
s2 := Sym(408)!(  3,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)
( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 59, 60)
( 63, 64)( 67, 68)( 69,137)( 70,138)( 71,140)( 72,139)( 73,141)( 74,142)
( 75,144)( 76,143)( 77,145)( 78,146)( 79,148)( 80,147)( 81,149)( 82,150)
( 83,152)( 84,151)( 85,153)( 86,154)( 87,156)( 88,155)( 89,157)( 90,158)
( 91,160)( 92,159)( 93,161)( 94,162)( 95,164)( 96,163)( 97,165)( 98,166)
( 99,168)(100,167)(101,169)(102,170)(103,172)(104,171)(105,173)(106,174)
(107,176)(108,175)(109,177)(110,178)(111,180)(112,179)(113,181)(114,182)
(115,184)(116,183)(117,185)(118,186)(119,188)(120,187)(121,189)(122,190)
(123,192)(124,191)(125,193)(126,194)(127,196)(128,195)(129,197)(130,198)
(131,200)(132,199)(133,201)(134,202)(135,204)(136,203)(207,208)(211,212)
(215,216)(219,220)(223,224)(227,228)(231,232)(235,236)(239,240)(243,244)
(247,248)(251,252)(255,256)(259,260)(263,264)(267,268)(271,272)(273,341)
(274,342)(275,344)(276,343)(277,345)(278,346)(279,348)(280,347)(281,349)
(282,350)(283,352)(284,351)(285,353)(286,354)(287,356)(288,355)(289,357)
(290,358)(291,360)(292,359)(293,361)(294,362)(295,364)(296,363)(297,365)
(298,366)(299,368)(300,367)(301,369)(302,370)(303,372)(304,371)(305,373)
(306,374)(307,376)(308,375)(309,377)(310,378)(311,380)(312,379)(313,381)
(314,382)(315,384)(316,383)(317,385)(318,386)(319,388)(320,387)(321,389)
(322,390)(323,392)(324,391)(325,393)(326,394)(327,396)(328,395)(329,397)
(330,398)(331,400)(332,399)(333,401)(334,402)(335,404)(336,403)(337,405)
(338,406)(339,408)(340,407);
s3 := Sym(408)!(  1, 69)(  2, 72)(  3, 71)(  4, 70)(  5, 73)(  6, 76)(  7, 75)
(  8, 74)(  9, 77)( 10, 80)( 11, 79)( 12, 78)( 13, 81)( 14, 84)( 15, 83)
( 16, 82)( 17, 85)( 18, 88)( 19, 87)( 20, 86)( 21, 89)( 22, 92)( 23, 91)
( 24, 90)( 25, 93)( 26, 96)( 27, 95)( 28, 94)( 29, 97)( 30,100)( 31, 99)
( 32, 98)( 33,101)( 34,104)( 35,103)( 36,102)( 37,105)( 38,108)( 39,107)
( 40,106)( 41,109)( 42,112)( 43,111)( 44,110)( 45,113)( 46,116)( 47,115)
( 48,114)( 49,117)( 50,120)( 51,119)( 52,118)( 53,121)( 54,124)( 55,123)
( 56,122)( 57,125)( 58,128)( 59,127)( 60,126)( 61,129)( 62,132)( 63,131)
( 64,130)( 65,133)( 66,136)( 67,135)( 68,134)(138,140)(142,144)(146,148)
(150,152)(154,156)(158,160)(162,164)(166,168)(170,172)(174,176)(178,180)
(182,184)(186,188)(190,192)(194,196)(198,200)(202,204)(205,273)(206,276)
(207,275)(208,274)(209,277)(210,280)(211,279)(212,278)(213,281)(214,284)
(215,283)(216,282)(217,285)(218,288)(219,287)(220,286)(221,289)(222,292)
(223,291)(224,290)(225,293)(226,296)(227,295)(228,294)(229,297)(230,300)
(231,299)(232,298)(233,301)(234,304)(235,303)(236,302)(237,305)(238,308)
(239,307)(240,306)(241,309)(242,312)(243,311)(244,310)(245,313)(246,316)
(247,315)(248,314)(249,317)(250,320)(251,319)(252,318)(253,321)(254,324)
(255,323)(256,322)(257,325)(258,328)(259,327)(260,326)(261,329)(262,332)
(263,331)(264,330)(265,333)(266,336)(267,335)(268,334)(269,337)(270,340)
(271,339)(272,338)(342,344)(346,348)(350,352)(354,356)(358,360)(362,364)
(366,368)(370,372)(374,376)(378,380)(382,384)(386,388)(390,392)(394,396)
(398,400)(402,404)(406,408);
poly := sub<Sym(408)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
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