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Polytope of Type {30,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,28}*1680a
Also Known As : {30,28|2}. if this polytope has another name.
Group : SmallGroup(1680,717)
Rank : 3
Schlafli Type : {30,28}
Number of vertices, edges, etc : 30, 420, 28
Order of s0s1s2 : 420
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 : {30,14}*840
   3-fold quotients : {10,28}*560
   5-fold quotients : {6,28}*336a
   6-fold quotients : {10,14}*280
   7-fold quotients : {30,4}*240a
   10-fold quotients : {6,14}*168
   14-fold quotients : {30,2}*120
   15-fold quotients : {2,28}*112
   21-fold quotients : {10,4}*80
   28-fold quotients : {15,2}*60
   30-fold quotients : {2,14}*56
   35-fold quotients : {6,4}*48a
   42-fold quotients : {10,2}*40
   60-fold quotients : {2,7}*28
   70-fold quotients : {6,2}*24
   84-fold quotients : {5,2}*20
   105-fold quotients : {2,4}*16
   140-fold quotients : {3,2}*12
   210-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  8, 29)(  9, 30)( 10, 31)( 11, 32)( 12, 33)( 13, 34)( 14, 35)( 15, 22)
( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 36, 71)( 37, 72)
( 38, 73)( 39, 74)( 40, 75)( 41, 76)( 42, 77)( 43, 99)( 44,100)( 45,101)
( 46,102)( 47,103)( 48,104)( 49,105)( 50, 92)( 51, 93)( 52, 94)( 53, 95)
( 54, 96)( 55, 97)( 56, 98)( 57, 85)( 58, 86)( 59, 87)( 60, 88)( 61, 89)
( 62, 90)( 63, 91)( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)( 69, 83)
( 70, 84)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)
(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)(141,176)
(142,177)(143,178)(144,179)(145,180)(146,181)(147,182)(148,204)(149,205)
(150,206)(151,207)(152,208)(153,209)(154,210)(155,197)(156,198)(157,199)
(158,200)(159,201)(160,202)(161,203)(162,190)(163,191)(164,192)(165,193)
(166,194)(167,195)(168,196)(169,183)(170,184)(171,185)(172,186)(173,187)
(174,188)(175,189)(218,239)(219,240)(220,241)(221,242)(222,243)(223,244)
(224,245)(225,232)(226,233)(227,234)(228,235)(229,236)(230,237)(231,238)
(246,281)(247,282)(248,283)(249,284)(250,285)(251,286)(252,287)(253,309)
(254,310)(255,311)(256,312)(257,313)(258,314)(259,315)(260,302)(261,303)
(262,304)(263,305)(264,306)(265,307)(266,308)(267,295)(268,296)(269,297)
(270,298)(271,299)(272,300)(273,301)(274,288)(275,289)(276,290)(277,291)
(278,292)(279,293)(280,294)(323,344)(324,345)(325,346)(326,347)(327,348)
(328,349)(329,350)(330,337)(331,338)(332,339)(333,340)(334,341)(335,342)
(336,343)(351,386)(352,387)(353,388)(354,389)(355,390)(356,391)(357,392)
(358,414)(359,415)(360,416)(361,417)(362,418)(363,419)(364,420)(365,407)
(366,408)(367,409)(368,410)(369,411)(370,412)(371,413)(372,400)(373,401)
(374,402)(375,403)(376,404)(377,405)(378,406)(379,393)(380,394)(381,395)
(382,396)(383,397)(384,398)(385,399);;
s1 := (  1, 43)(  2, 49)(  3, 48)(  4, 47)(  5, 46)(  6, 45)(  7, 44)(  8, 36)
(  9, 42)( 10, 41)( 11, 40)( 12, 39)( 13, 38)( 14, 37)( 15, 64)( 16, 70)
( 17, 69)( 18, 68)( 19, 67)( 20, 66)( 21, 65)( 22, 57)( 23, 63)( 24, 62)
( 25, 61)( 26, 60)( 27, 59)( 28, 58)( 29, 50)( 30, 56)( 31, 55)( 32, 54)
( 33, 53)( 34, 52)( 35, 51)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)
( 76, 80)( 77, 79)( 85, 99)( 86,105)( 87,104)( 88,103)( 89,102)( 90,101)
( 91,100)( 93, 98)( 94, 97)( 95, 96)(106,148)(107,154)(108,153)(109,152)
(110,151)(111,150)(112,149)(113,141)(114,147)(115,146)(116,145)(117,144)
(118,143)(119,142)(120,169)(121,175)(122,174)(123,173)(124,172)(125,171)
(126,170)(127,162)(128,168)(129,167)(130,166)(131,165)(132,164)(133,163)
(134,155)(135,161)(136,160)(137,159)(138,158)(139,157)(140,156)(176,183)
(177,189)(178,188)(179,187)(180,186)(181,185)(182,184)(190,204)(191,210)
(192,209)(193,208)(194,207)(195,206)(196,205)(198,203)(199,202)(200,201)
(211,358)(212,364)(213,363)(214,362)(215,361)(216,360)(217,359)(218,351)
(219,357)(220,356)(221,355)(222,354)(223,353)(224,352)(225,379)(226,385)
(227,384)(228,383)(229,382)(230,381)(231,380)(232,372)(233,378)(234,377)
(235,376)(236,375)(237,374)(238,373)(239,365)(240,371)(241,370)(242,369)
(243,368)(244,367)(245,366)(246,323)(247,329)(248,328)(249,327)(250,326)
(251,325)(252,324)(253,316)(254,322)(255,321)(256,320)(257,319)(258,318)
(259,317)(260,344)(261,350)(262,349)(263,348)(264,347)(265,346)(266,345)
(267,337)(268,343)(269,342)(270,341)(271,340)(272,339)(273,338)(274,330)
(275,336)(276,335)(277,334)(278,333)(279,332)(280,331)(281,393)(282,399)
(283,398)(284,397)(285,396)(286,395)(287,394)(288,386)(289,392)(290,391)
(291,390)(292,389)(293,388)(294,387)(295,414)(296,420)(297,419)(298,418)
(299,417)(300,416)(301,415)(302,407)(303,413)(304,412)(305,411)(306,410)
(307,409)(308,408)(309,400)(310,406)(311,405)(312,404)(313,403)(314,402)
(315,401);;
s2 := (  1,212)(  2,211)(  3,217)(  4,216)(  5,215)(  6,214)(  7,213)(  8,219)
(  9,218)( 10,224)( 11,223)( 12,222)( 13,221)( 14,220)( 15,226)( 16,225)
( 17,231)( 18,230)( 19,229)( 20,228)( 21,227)( 22,233)( 23,232)( 24,238)
( 25,237)( 26,236)( 27,235)( 28,234)( 29,240)( 30,239)( 31,245)( 32,244)
( 33,243)( 34,242)( 35,241)( 36,247)( 37,246)( 38,252)( 39,251)( 40,250)
( 41,249)( 42,248)( 43,254)( 44,253)( 45,259)( 46,258)( 47,257)( 48,256)
( 49,255)( 50,261)( 51,260)( 52,266)( 53,265)( 54,264)( 55,263)( 56,262)
( 57,268)( 58,267)( 59,273)( 60,272)( 61,271)( 62,270)( 63,269)( 64,275)
( 65,274)( 66,280)( 67,279)( 68,278)( 69,277)( 70,276)( 71,282)( 72,281)
( 73,287)( 74,286)( 75,285)( 76,284)( 77,283)( 78,289)( 79,288)( 80,294)
( 81,293)( 82,292)( 83,291)( 84,290)( 85,296)( 86,295)( 87,301)( 88,300)
( 89,299)( 90,298)( 91,297)( 92,303)( 93,302)( 94,308)( 95,307)( 96,306)
( 97,305)( 98,304)( 99,310)(100,309)(101,315)(102,314)(103,313)(104,312)
(105,311)(106,317)(107,316)(108,322)(109,321)(110,320)(111,319)(112,318)
(113,324)(114,323)(115,329)(116,328)(117,327)(118,326)(119,325)(120,331)
(121,330)(122,336)(123,335)(124,334)(125,333)(126,332)(127,338)(128,337)
(129,343)(130,342)(131,341)(132,340)(133,339)(134,345)(135,344)(136,350)
(137,349)(138,348)(139,347)(140,346)(141,352)(142,351)(143,357)(144,356)
(145,355)(146,354)(147,353)(148,359)(149,358)(150,364)(151,363)(152,362)
(153,361)(154,360)(155,366)(156,365)(157,371)(158,370)(159,369)(160,368)
(161,367)(162,373)(163,372)(164,378)(165,377)(166,376)(167,375)(168,374)
(169,380)(170,379)(171,385)(172,384)(173,383)(174,382)(175,381)(176,387)
(177,386)(178,392)(179,391)(180,390)(181,389)(182,388)(183,394)(184,393)
(185,399)(186,398)(187,397)(188,396)(189,395)(190,401)(191,400)(192,406)
(193,405)(194,404)(195,403)(196,402)(197,408)(198,407)(199,413)(200,412)
(201,411)(202,410)(203,409)(204,415)(205,414)(206,420)(207,419)(208,418)
(209,417)(210,416);;
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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(420)!(  8, 29)(  9, 30)( 10, 31)( 11, 32)( 12, 33)( 13, 34)( 14, 35)
( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 36, 71)
( 37, 72)( 38, 73)( 39, 74)( 40, 75)( 41, 76)( 42, 77)( 43, 99)( 44,100)
( 45,101)( 46,102)( 47,103)( 48,104)( 49,105)( 50, 92)( 51, 93)( 52, 94)
( 53, 95)( 54, 96)( 55, 97)( 56, 98)( 57, 85)( 58, 86)( 59, 87)( 60, 88)
( 61, 89)( 62, 90)( 63, 91)( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)
( 69, 83)( 70, 84)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)
(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)
(141,176)(142,177)(143,178)(144,179)(145,180)(146,181)(147,182)(148,204)
(149,205)(150,206)(151,207)(152,208)(153,209)(154,210)(155,197)(156,198)
(157,199)(158,200)(159,201)(160,202)(161,203)(162,190)(163,191)(164,192)
(165,193)(166,194)(167,195)(168,196)(169,183)(170,184)(171,185)(172,186)
(173,187)(174,188)(175,189)(218,239)(219,240)(220,241)(221,242)(222,243)
(223,244)(224,245)(225,232)(226,233)(227,234)(228,235)(229,236)(230,237)
(231,238)(246,281)(247,282)(248,283)(249,284)(250,285)(251,286)(252,287)
(253,309)(254,310)(255,311)(256,312)(257,313)(258,314)(259,315)(260,302)
(261,303)(262,304)(263,305)(264,306)(265,307)(266,308)(267,295)(268,296)
(269,297)(270,298)(271,299)(272,300)(273,301)(274,288)(275,289)(276,290)
(277,291)(278,292)(279,293)(280,294)(323,344)(324,345)(325,346)(326,347)
(327,348)(328,349)(329,350)(330,337)(331,338)(332,339)(333,340)(334,341)
(335,342)(336,343)(351,386)(352,387)(353,388)(354,389)(355,390)(356,391)
(357,392)(358,414)(359,415)(360,416)(361,417)(362,418)(363,419)(364,420)
(365,407)(366,408)(367,409)(368,410)(369,411)(370,412)(371,413)(372,400)
(373,401)(374,402)(375,403)(376,404)(377,405)(378,406)(379,393)(380,394)
(381,395)(382,396)(383,397)(384,398)(385,399);
s1 := Sym(420)!(  1, 43)(  2, 49)(  3, 48)(  4, 47)(  5, 46)(  6, 45)(  7, 44)
(  8, 36)(  9, 42)( 10, 41)( 11, 40)( 12, 39)( 13, 38)( 14, 37)( 15, 64)
( 16, 70)( 17, 69)( 18, 68)( 19, 67)( 20, 66)( 21, 65)( 22, 57)( 23, 63)
( 24, 62)( 25, 61)( 26, 60)( 27, 59)( 28, 58)( 29, 50)( 30, 56)( 31, 55)
( 32, 54)( 33, 53)( 34, 52)( 35, 51)( 71, 78)( 72, 84)( 73, 83)( 74, 82)
( 75, 81)( 76, 80)( 77, 79)( 85, 99)( 86,105)( 87,104)( 88,103)( 89,102)
( 90,101)( 91,100)( 93, 98)( 94, 97)( 95, 96)(106,148)(107,154)(108,153)
(109,152)(110,151)(111,150)(112,149)(113,141)(114,147)(115,146)(116,145)
(117,144)(118,143)(119,142)(120,169)(121,175)(122,174)(123,173)(124,172)
(125,171)(126,170)(127,162)(128,168)(129,167)(130,166)(131,165)(132,164)
(133,163)(134,155)(135,161)(136,160)(137,159)(138,158)(139,157)(140,156)
(176,183)(177,189)(178,188)(179,187)(180,186)(181,185)(182,184)(190,204)
(191,210)(192,209)(193,208)(194,207)(195,206)(196,205)(198,203)(199,202)
(200,201)(211,358)(212,364)(213,363)(214,362)(215,361)(216,360)(217,359)
(218,351)(219,357)(220,356)(221,355)(222,354)(223,353)(224,352)(225,379)
(226,385)(227,384)(228,383)(229,382)(230,381)(231,380)(232,372)(233,378)
(234,377)(235,376)(236,375)(237,374)(238,373)(239,365)(240,371)(241,370)
(242,369)(243,368)(244,367)(245,366)(246,323)(247,329)(248,328)(249,327)
(250,326)(251,325)(252,324)(253,316)(254,322)(255,321)(256,320)(257,319)
(258,318)(259,317)(260,344)(261,350)(262,349)(263,348)(264,347)(265,346)
(266,345)(267,337)(268,343)(269,342)(270,341)(271,340)(272,339)(273,338)
(274,330)(275,336)(276,335)(277,334)(278,333)(279,332)(280,331)(281,393)
(282,399)(283,398)(284,397)(285,396)(286,395)(287,394)(288,386)(289,392)
(290,391)(291,390)(292,389)(293,388)(294,387)(295,414)(296,420)(297,419)
(298,418)(299,417)(300,416)(301,415)(302,407)(303,413)(304,412)(305,411)
(306,410)(307,409)(308,408)(309,400)(310,406)(311,405)(312,404)(313,403)
(314,402)(315,401);
s2 := Sym(420)!(  1,212)(  2,211)(  3,217)(  4,216)(  5,215)(  6,214)(  7,213)
(  8,219)(  9,218)( 10,224)( 11,223)( 12,222)( 13,221)( 14,220)( 15,226)
( 16,225)( 17,231)( 18,230)( 19,229)( 20,228)( 21,227)( 22,233)( 23,232)
( 24,238)( 25,237)( 26,236)( 27,235)( 28,234)( 29,240)( 30,239)( 31,245)
( 32,244)( 33,243)( 34,242)( 35,241)( 36,247)( 37,246)( 38,252)( 39,251)
( 40,250)( 41,249)( 42,248)( 43,254)( 44,253)( 45,259)( 46,258)( 47,257)
( 48,256)( 49,255)( 50,261)( 51,260)( 52,266)( 53,265)( 54,264)( 55,263)
( 56,262)( 57,268)( 58,267)( 59,273)( 60,272)( 61,271)( 62,270)( 63,269)
( 64,275)( 65,274)( 66,280)( 67,279)( 68,278)( 69,277)( 70,276)( 71,282)
( 72,281)( 73,287)( 74,286)( 75,285)( 76,284)( 77,283)( 78,289)( 79,288)
( 80,294)( 81,293)( 82,292)( 83,291)( 84,290)( 85,296)( 86,295)( 87,301)
( 88,300)( 89,299)( 90,298)( 91,297)( 92,303)( 93,302)( 94,308)( 95,307)
( 96,306)( 97,305)( 98,304)( 99,310)(100,309)(101,315)(102,314)(103,313)
(104,312)(105,311)(106,317)(107,316)(108,322)(109,321)(110,320)(111,319)
(112,318)(113,324)(114,323)(115,329)(116,328)(117,327)(118,326)(119,325)
(120,331)(121,330)(122,336)(123,335)(124,334)(125,333)(126,332)(127,338)
(128,337)(129,343)(130,342)(131,341)(132,340)(133,339)(134,345)(135,344)
(136,350)(137,349)(138,348)(139,347)(140,346)(141,352)(142,351)(143,357)
(144,356)(145,355)(146,354)(147,353)(148,359)(149,358)(150,364)(151,363)
(152,362)(153,361)(154,360)(155,366)(156,365)(157,371)(158,370)(159,369)
(160,368)(161,367)(162,373)(163,372)(164,378)(165,377)(166,376)(167,375)
(168,374)(169,380)(170,379)(171,385)(172,384)(173,383)(174,382)(175,381)
(176,387)(177,386)(178,392)(179,391)(180,390)(181,389)(182,388)(183,394)
(184,393)(185,399)(186,398)(187,397)(188,396)(189,395)(190,401)(191,400)
(192,406)(193,405)(194,404)(195,403)(196,402)(197,408)(198,407)(199,413)
(200,412)(201,411)(202,410)(203,409)(204,415)(205,414)(206,420)(207,419)
(208,418)(209,417)(210,416);
poly := sub<Sym(420)|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*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 >; 
 
References : None.
to this polytope