Polytope of Type {12,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,10}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240399)
Rank : 3
Schlafli Type : {12,10}
Number of vertices, edges, etc : 96, 480, 80
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
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 : {12,10}*960e
   3-fold quotients : {4,10}*640b
   6-fold quotients : {4,5}*320, {4,10}*320a, {4,10}*320b
   12-fold quotients : {4,5}*160
   16-fold quotients : {6,10}*120
   48-fold quotients : {2,10}*40
   80-fold quotients : {6,2}*24
   96-fold quotients : {2,5}*20
   160-fold quotients : {3,2}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81,169)( 82,170)( 83,171)( 84,172)( 85,173)( 86,174)( 87,175)( 88,176)
( 89,161)( 90,162)( 91,163)( 92,164)( 93,165)( 94,166)( 95,167)( 96,168)
( 97,185)( 98,186)( 99,187)(100,188)(101,189)(102,190)(103,191)(104,192)
(105,177)(106,178)(107,179)(108,180)(109,181)(110,182)(111,183)(112,184)
(113,201)(114,202)(115,203)(116,204)(117,205)(118,206)(119,207)(120,208)
(121,193)(122,194)(123,195)(124,196)(125,197)(126,198)(127,199)(128,200)
(129,217)(130,218)(131,219)(132,220)(133,221)(134,222)(135,223)(136,224)
(137,209)(138,210)(139,211)(140,212)(141,213)(142,214)(143,215)(144,216)
(145,233)(146,234)(147,235)(148,236)(149,237)(150,238)(151,239)(152,240)
(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)
(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)
(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)
(321,409)(322,410)(323,411)(324,412)(325,413)(326,414)(327,415)(328,416)
(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)(336,408)
(337,425)(338,426)(339,427)(340,428)(341,429)(342,430)(343,431)(344,432)
(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)(352,424)
(353,441)(354,442)(355,443)(356,444)(357,445)(358,446)(359,447)(360,448)
(361,433)(362,434)(363,435)(364,436)(365,437)(366,438)(367,439)(368,440)
(369,457)(370,458)(371,459)(372,460)(373,461)(374,462)(375,463)(376,464)
(377,449)(378,450)(379,451)(380,452)(381,453)(382,454)(383,455)(384,456)
(385,473)(386,474)(387,475)(388,476)(389,477)(390,478)(391,479)(392,480)
(393,465)(394,466)(395,467)(396,468)(397,469)(398,470)(399,471)(400,472);;
s1 := (  1, 81)(  2, 82)(  3, 84)(  4, 83)(  5, 85)(  6, 86)(  7, 88)(  8, 87)
(  9, 94)( 10, 93)( 11, 95)( 12, 96)( 13, 90)( 14, 89)( 15, 91)( 16, 92)
( 17,145)( 18,146)( 19,148)( 20,147)( 21,149)( 22,150)( 23,152)( 24,151)
( 25,158)( 26,157)( 27,159)( 28,160)( 29,154)( 30,153)( 31,155)( 32,156)
( 33,129)( 34,130)( 35,132)( 36,131)( 37,133)( 38,134)( 39,136)( 40,135)
( 41,142)( 42,141)( 43,143)( 44,144)( 45,138)( 46,137)( 47,139)( 48,140)
( 49,113)( 50,114)( 51,116)( 52,115)( 53,117)( 54,118)( 55,120)( 56,119)
( 57,126)( 58,125)( 59,127)( 60,128)( 61,122)( 62,121)( 63,123)( 64,124)
( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,101)( 70,102)( 71,104)( 72,103)
( 73,110)( 74,109)( 75,111)( 76,112)( 77,106)( 78,105)( 79,107)( 80,108)
(163,164)(167,168)(169,174)(170,173)(171,175)(172,176)(177,225)(178,226)
(179,228)(180,227)(181,229)(182,230)(183,232)(184,231)(185,238)(186,237)
(187,239)(188,240)(189,234)(190,233)(191,235)(192,236)(193,209)(194,210)
(195,212)(196,211)(197,213)(198,214)(199,216)(200,215)(201,222)(202,221)
(203,223)(204,224)(205,218)(206,217)(207,219)(208,220)(241,321)(242,322)
(243,324)(244,323)(245,325)(246,326)(247,328)(248,327)(249,334)(250,333)
(251,335)(252,336)(253,330)(254,329)(255,331)(256,332)(257,385)(258,386)
(259,388)(260,387)(261,389)(262,390)(263,392)(264,391)(265,398)(266,397)
(267,399)(268,400)(269,394)(270,393)(271,395)(272,396)(273,369)(274,370)
(275,372)(276,371)(277,373)(278,374)(279,376)(280,375)(281,382)(282,381)
(283,383)(284,384)(285,378)(286,377)(287,379)(288,380)(289,353)(290,354)
(291,356)(292,355)(293,357)(294,358)(295,360)(296,359)(297,366)(298,365)
(299,367)(300,368)(301,362)(302,361)(303,363)(304,364)(305,337)(306,338)
(307,340)(308,339)(309,341)(310,342)(311,344)(312,343)(313,350)(314,349)
(315,351)(316,352)(317,346)(318,345)(319,347)(320,348)(403,404)(407,408)
(409,414)(410,413)(411,415)(412,416)(417,465)(418,466)(419,468)(420,467)
(421,469)(422,470)(423,472)(424,471)(425,478)(426,477)(427,479)(428,480)
(429,474)(430,473)(431,475)(432,476)(433,449)(434,450)(435,452)(436,451)
(437,453)(438,454)(439,456)(440,455)(441,462)(442,461)(443,463)(444,464)
(445,458)(446,457)(447,459)(448,460);;
s2 := (  1,289)(  2,298)(  3,299)(  4,292)(  5,296)(  6,303)(  7,302)(  8,293)
(  9,297)( 10,290)( 11,291)( 12,300)( 13,304)( 14,295)( 15,294)( 16,301)
( 17,273)( 18,282)( 19,283)( 20,276)( 21,280)( 22,287)( 23,286)( 24,277)
( 25,281)( 26,274)( 27,275)( 28,284)( 29,288)( 30,279)( 31,278)( 32,285)
( 33,257)( 34,266)( 35,267)( 36,260)( 37,264)( 38,271)( 39,270)( 40,261)
( 41,265)( 42,258)( 43,259)( 44,268)( 45,272)( 46,263)( 47,262)( 48,269)
( 49,241)( 50,250)( 51,251)( 52,244)( 53,248)( 54,255)( 55,254)( 56,245)
( 57,249)( 58,242)( 59,243)( 60,252)( 61,256)( 62,247)( 63,246)( 64,253)
( 65,305)( 66,314)( 67,315)( 68,308)( 69,312)( 70,319)( 71,318)( 72,309)
( 73,313)( 74,306)( 75,307)( 76,316)( 77,320)( 78,311)( 79,310)( 80,317)
( 81,369)( 82,378)( 83,379)( 84,372)( 85,376)( 86,383)( 87,382)( 88,373)
( 89,377)( 90,370)( 91,371)( 92,380)( 93,384)( 94,375)( 95,374)( 96,381)
( 97,353)( 98,362)( 99,363)(100,356)(101,360)(102,367)(103,366)(104,357)
(105,361)(106,354)(107,355)(108,364)(109,368)(110,359)(111,358)(112,365)
(113,337)(114,346)(115,347)(116,340)(117,344)(118,351)(119,350)(120,341)
(121,345)(122,338)(123,339)(124,348)(125,352)(126,343)(127,342)(128,349)
(129,321)(130,330)(131,331)(132,324)(133,328)(134,335)(135,334)(136,325)
(137,329)(138,322)(139,323)(140,332)(141,336)(142,327)(143,326)(144,333)
(145,385)(146,394)(147,395)(148,388)(149,392)(150,399)(151,398)(152,389)
(153,393)(154,386)(155,387)(156,396)(157,400)(158,391)(159,390)(160,397)
(161,449)(162,458)(163,459)(164,452)(165,456)(166,463)(167,462)(168,453)
(169,457)(170,450)(171,451)(172,460)(173,464)(174,455)(175,454)(176,461)
(177,433)(178,442)(179,443)(180,436)(181,440)(182,447)(183,446)(184,437)
(185,441)(186,434)(187,435)(188,444)(189,448)(190,439)(191,438)(192,445)
(193,417)(194,426)(195,427)(196,420)(197,424)(198,431)(199,430)(200,421)
(201,425)(202,418)(203,419)(204,428)(205,432)(206,423)(207,422)(208,429)
(209,401)(210,410)(211,411)(212,404)(213,408)(214,415)(215,414)(216,405)
(217,409)(218,402)(219,403)(220,412)(221,416)(222,407)(223,406)(224,413)
(225,465)(226,474)(227,475)(228,468)(229,472)(230,479)(231,478)(232,469)
(233,473)(234,466)(235,467)(236,476)(237,480)(238,471)(239,470)(240,477);;
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*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, 
s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(480)!(  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)
(  8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81,169)( 82,170)( 83,171)( 84,172)( 85,173)( 86,174)( 87,175)
( 88,176)( 89,161)( 90,162)( 91,163)( 92,164)( 93,165)( 94,166)( 95,167)
( 96,168)( 97,185)( 98,186)( 99,187)(100,188)(101,189)(102,190)(103,191)
(104,192)(105,177)(106,178)(107,179)(108,180)(109,181)(110,182)(111,183)
(112,184)(113,201)(114,202)(115,203)(116,204)(117,205)(118,206)(119,207)
(120,208)(121,193)(122,194)(123,195)(124,196)(125,197)(126,198)(127,199)
(128,200)(129,217)(130,218)(131,219)(132,220)(133,221)(134,222)(135,223)
(136,224)(137,209)(138,210)(139,211)(140,212)(141,213)(142,214)(143,215)
(144,216)(145,233)(146,234)(147,235)(148,236)(149,237)(150,238)(151,239)
(152,240)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)
(160,232)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288)(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)
(296,304)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)
(312,320)(321,409)(322,410)(323,411)(324,412)(325,413)(326,414)(327,415)
(328,416)(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)
(336,408)(337,425)(338,426)(339,427)(340,428)(341,429)(342,430)(343,431)
(344,432)(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)
(352,424)(353,441)(354,442)(355,443)(356,444)(357,445)(358,446)(359,447)
(360,448)(361,433)(362,434)(363,435)(364,436)(365,437)(366,438)(367,439)
(368,440)(369,457)(370,458)(371,459)(372,460)(373,461)(374,462)(375,463)
(376,464)(377,449)(378,450)(379,451)(380,452)(381,453)(382,454)(383,455)
(384,456)(385,473)(386,474)(387,475)(388,476)(389,477)(390,478)(391,479)
(392,480)(393,465)(394,466)(395,467)(396,468)(397,469)(398,470)(399,471)
(400,472);
s1 := Sym(480)!(  1, 81)(  2, 82)(  3, 84)(  4, 83)(  5, 85)(  6, 86)(  7, 88)
(  8, 87)(  9, 94)( 10, 93)( 11, 95)( 12, 96)( 13, 90)( 14, 89)( 15, 91)
( 16, 92)( 17,145)( 18,146)( 19,148)( 20,147)( 21,149)( 22,150)( 23,152)
( 24,151)( 25,158)( 26,157)( 27,159)( 28,160)( 29,154)( 30,153)( 31,155)
( 32,156)( 33,129)( 34,130)( 35,132)( 36,131)( 37,133)( 38,134)( 39,136)
( 40,135)( 41,142)( 42,141)( 43,143)( 44,144)( 45,138)( 46,137)( 47,139)
( 48,140)( 49,113)( 50,114)( 51,116)( 52,115)( 53,117)( 54,118)( 55,120)
( 56,119)( 57,126)( 58,125)( 59,127)( 60,128)( 61,122)( 62,121)( 63,123)
( 64,124)( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,101)( 70,102)( 71,104)
( 72,103)( 73,110)( 74,109)( 75,111)( 76,112)( 77,106)( 78,105)( 79,107)
( 80,108)(163,164)(167,168)(169,174)(170,173)(171,175)(172,176)(177,225)
(178,226)(179,228)(180,227)(181,229)(182,230)(183,232)(184,231)(185,238)
(186,237)(187,239)(188,240)(189,234)(190,233)(191,235)(192,236)(193,209)
(194,210)(195,212)(196,211)(197,213)(198,214)(199,216)(200,215)(201,222)
(202,221)(203,223)(204,224)(205,218)(206,217)(207,219)(208,220)(241,321)
(242,322)(243,324)(244,323)(245,325)(246,326)(247,328)(248,327)(249,334)
(250,333)(251,335)(252,336)(253,330)(254,329)(255,331)(256,332)(257,385)
(258,386)(259,388)(260,387)(261,389)(262,390)(263,392)(264,391)(265,398)
(266,397)(267,399)(268,400)(269,394)(270,393)(271,395)(272,396)(273,369)
(274,370)(275,372)(276,371)(277,373)(278,374)(279,376)(280,375)(281,382)
(282,381)(283,383)(284,384)(285,378)(286,377)(287,379)(288,380)(289,353)
(290,354)(291,356)(292,355)(293,357)(294,358)(295,360)(296,359)(297,366)
(298,365)(299,367)(300,368)(301,362)(302,361)(303,363)(304,364)(305,337)
(306,338)(307,340)(308,339)(309,341)(310,342)(311,344)(312,343)(313,350)
(314,349)(315,351)(316,352)(317,346)(318,345)(319,347)(320,348)(403,404)
(407,408)(409,414)(410,413)(411,415)(412,416)(417,465)(418,466)(419,468)
(420,467)(421,469)(422,470)(423,472)(424,471)(425,478)(426,477)(427,479)
(428,480)(429,474)(430,473)(431,475)(432,476)(433,449)(434,450)(435,452)
(436,451)(437,453)(438,454)(439,456)(440,455)(441,462)(442,461)(443,463)
(444,464)(445,458)(446,457)(447,459)(448,460);
s2 := Sym(480)!(  1,289)(  2,298)(  3,299)(  4,292)(  5,296)(  6,303)(  7,302)
(  8,293)(  9,297)( 10,290)( 11,291)( 12,300)( 13,304)( 14,295)( 15,294)
( 16,301)( 17,273)( 18,282)( 19,283)( 20,276)( 21,280)( 22,287)( 23,286)
( 24,277)( 25,281)( 26,274)( 27,275)( 28,284)( 29,288)( 30,279)( 31,278)
( 32,285)( 33,257)( 34,266)( 35,267)( 36,260)( 37,264)( 38,271)( 39,270)
( 40,261)( 41,265)( 42,258)( 43,259)( 44,268)( 45,272)( 46,263)( 47,262)
( 48,269)( 49,241)( 50,250)( 51,251)( 52,244)( 53,248)( 54,255)( 55,254)
( 56,245)( 57,249)( 58,242)( 59,243)( 60,252)( 61,256)( 62,247)( 63,246)
( 64,253)( 65,305)( 66,314)( 67,315)( 68,308)( 69,312)( 70,319)( 71,318)
( 72,309)( 73,313)( 74,306)( 75,307)( 76,316)( 77,320)( 78,311)( 79,310)
( 80,317)( 81,369)( 82,378)( 83,379)( 84,372)( 85,376)( 86,383)( 87,382)
( 88,373)( 89,377)( 90,370)( 91,371)( 92,380)( 93,384)( 94,375)( 95,374)
( 96,381)( 97,353)( 98,362)( 99,363)(100,356)(101,360)(102,367)(103,366)
(104,357)(105,361)(106,354)(107,355)(108,364)(109,368)(110,359)(111,358)
(112,365)(113,337)(114,346)(115,347)(116,340)(117,344)(118,351)(119,350)
(120,341)(121,345)(122,338)(123,339)(124,348)(125,352)(126,343)(127,342)
(128,349)(129,321)(130,330)(131,331)(132,324)(133,328)(134,335)(135,334)
(136,325)(137,329)(138,322)(139,323)(140,332)(141,336)(142,327)(143,326)
(144,333)(145,385)(146,394)(147,395)(148,388)(149,392)(150,399)(151,398)
(152,389)(153,393)(154,386)(155,387)(156,396)(157,400)(158,391)(159,390)
(160,397)(161,449)(162,458)(163,459)(164,452)(165,456)(166,463)(167,462)
(168,453)(169,457)(170,450)(171,451)(172,460)(173,464)(174,455)(175,454)
(176,461)(177,433)(178,442)(179,443)(180,436)(181,440)(182,447)(183,446)
(184,437)(185,441)(186,434)(187,435)(188,444)(189,448)(190,439)(191,438)
(192,445)(193,417)(194,426)(195,427)(196,420)(197,424)(198,431)(199,430)
(200,421)(201,425)(202,418)(203,419)(204,428)(205,432)(206,423)(207,422)
(208,429)(209,401)(210,410)(211,411)(212,404)(213,408)(214,415)(215,414)
(216,405)(217,409)(218,402)(219,403)(220,412)(221,416)(222,407)(223,406)
(224,413)(225,465)(226,474)(227,475)(228,468)(229,472)(230,479)(231,478)
(232,469)(233,473)(234,466)(235,467)(236,476)(237,480)(238,471)(239,470)
(240,477);
poly := sub<Sym(480)|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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*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, 
s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s0*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 >;
References : None.
to this polytope