Polytope of Type {6,146}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,146}*1752
Also Known As : {6,146|2}. if this polytope has another name.
Group : SmallGroup(1752,57)
Rank : 3
Schlafli Type : {6,146}
Number of vertices, edges, etc : 6, 438, 146
Order of s0s1s2 : 438
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) :
3-fold quotients : {2,146}*584
6-fold quotients : {2,73}*292
73-fold quotients : {6,2}*24
146-fold quotients : {3,2}*12
219-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 74,147)( 75,148)( 76,149)( 77,150)( 78,151)( 79,152)( 80,153)( 81,154)
( 82,155)( 83,156)( 84,157)( 85,158)( 86,159)( 87,160)( 88,161)( 89,162)
( 90,163)( 91,164)( 92,165)( 93,166)( 94,167)( 95,168)( 96,169)( 97,170)
( 98,171)( 99,172)(100,173)(101,174)(102,175)(103,176)(104,177)(105,178)
(106,179)(107,180)(108,181)(109,182)(110,183)(111,184)(112,185)(113,186)
(114,187)(115,188)(116,189)(117,190)(118,191)(119,192)(120,193)(121,194)
(122,195)(123,196)(124,197)(125,198)(126,199)(127,200)(128,201)(129,202)
(130,203)(131,204)(132,205)(133,206)(134,207)(135,208)(136,209)(137,210)
(138,211)(139,212)(140,213)(141,214)(142,215)(143,216)(144,217)(145,218)
(146,219)(293,366)(294,367)(295,368)(296,369)(297,370)(298,371)(299,372)
(300,373)(301,374)(302,375)(303,376)(304,377)(305,378)(306,379)(307,380)
(308,381)(309,382)(310,383)(311,384)(312,385)(313,386)(314,387)(315,388)
(316,389)(317,390)(318,391)(319,392)(320,393)(321,394)(322,395)(323,396)
(324,397)(325,398)(326,399)(327,400)(328,401)(329,402)(330,403)(331,404)
(332,405)(333,406)(334,407)(335,408)(336,409)(337,410)(338,411)(339,412)
(340,413)(341,414)(342,415)(343,416)(344,417)(345,418)(346,419)(347,420)
(348,421)(349,422)(350,423)(351,424)(352,425)(353,426)(354,427)(355,428)
(356,429)(357,430)(358,431)(359,432)(360,433)(361,434)(362,435)(363,436)
(364,437)(365,438);;
s1 := ( 1, 74)( 2,146)( 3,145)( 4,144)( 5,143)( 6,142)( 7,141)( 8,140)
( 9,139)( 10,138)( 11,137)( 12,136)( 13,135)( 14,134)( 15,133)( 16,132)
( 17,131)( 18,130)( 19,129)( 20,128)( 21,127)( 22,126)( 23,125)( 24,124)
( 25,123)( 26,122)( 27,121)( 28,120)( 29,119)( 30,118)( 31,117)( 32,116)
( 33,115)( 34,114)( 35,113)( 36,112)( 37,111)( 38,110)( 39,109)( 40,108)
( 41,107)( 42,106)( 43,105)( 44,104)( 45,103)( 46,102)( 47,101)( 48,100)
( 49, 99)( 50, 98)( 51, 97)( 52, 96)( 53, 95)( 54, 94)( 55, 93)( 56, 92)
( 57, 91)( 58, 90)( 59, 89)( 60, 88)( 61, 87)( 62, 86)( 63, 85)( 64, 84)
( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)
( 73, 75)(148,219)(149,218)(150,217)(151,216)(152,215)(153,214)(154,213)
(155,212)(156,211)(157,210)(158,209)(159,208)(160,207)(161,206)(162,205)
(163,204)(164,203)(165,202)(166,201)(167,200)(168,199)(169,198)(170,197)
(171,196)(172,195)(173,194)(174,193)(175,192)(176,191)(177,190)(178,189)
(179,188)(180,187)(181,186)(182,185)(183,184)(220,293)(221,365)(222,364)
(223,363)(224,362)(225,361)(226,360)(227,359)(228,358)(229,357)(230,356)
(231,355)(232,354)(233,353)(234,352)(235,351)(236,350)(237,349)(238,348)
(239,347)(240,346)(241,345)(242,344)(243,343)(244,342)(245,341)(246,340)
(247,339)(248,338)(249,337)(250,336)(251,335)(252,334)(253,333)(254,332)
(255,331)(256,330)(257,329)(258,328)(259,327)(260,326)(261,325)(262,324)
(263,323)(264,322)(265,321)(266,320)(267,319)(268,318)(269,317)(270,316)
(271,315)(272,314)(273,313)(274,312)(275,311)(276,310)(277,309)(278,308)
(279,307)(280,306)(281,305)(282,304)(283,303)(284,302)(285,301)(286,300)
(287,299)(288,298)(289,297)(290,296)(291,295)(292,294)(367,438)(368,437)
(369,436)(370,435)(371,434)(372,433)(373,432)(374,431)(375,430)(376,429)
(377,428)(378,427)(379,426)(380,425)(381,424)(382,423)(383,422)(384,421)
(385,420)(386,419)(387,418)(388,417)(389,416)(390,415)(391,414)(392,413)
(393,412)(394,411)(395,410)(396,409)(397,408)(398,407)(399,406)(400,405)
(401,404)(402,403);;
s2 := ( 1,221)( 2,220)( 3,292)( 4,291)( 5,290)( 6,289)( 7,288)( 8,287)
( 9,286)( 10,285)( 11,284)( 12,283)( 13,282)( 14,281)( 15,280)( 16,279)
( 17,278)( 18,277)( 19,276)( 20,275)( 21,274)( 22,273)( 23,272)( 24,271)
( 25,270)( 26,269)( 27,268)( 28,267)( 29,266)( 30,265)( 31,264)( 32,263)
( 33,262)( 34,261)( 35,260)( 36,259)( 37,258)( 38,257)( 39,256)( 40,255)
( 41,254)( 42,253)( 43,252)( 44,251)( 45,250)( 46,249)( 47,248)( 48,247)
( 49,246)( 50,245)( 51,244)( 52,243)( 53,242)( 54,241)( 55,240)( 56,239)
( 57,238)( 58,237)( 59,236)( 60,235)( 61,234)( 62,233)( 63,232)( 64,231)
( 65,230)( 66,229)( 67,228)( 68,227)( 69,226)( 70,225)( 71,224)( 72,223)
( 73,222)( 74,294)( 75,293)( 76,365)( 77,364)( 78,363)( 79,362)( 80,361)
( 81,360)( 82,359)( 83,358)( 84,357)( 85,356)( 86,355)( 87,354)( 88,353)
( 89,352)( 90,351)( 91,350)( 92,349)( 93,348)( 94,347)( 95,346)( 96,345)
( 97,344)( 98,343)( 99,342)(100,341)(101,340)(102,339)(103,338)(104,337)
(105,336)(106,335)(107,334)(108,333)(109,332)(110,331)(111,330)(112,329)
(113,328)(114,327)(115,326)(116,325)(117,324)(118,323)(119,322)(120,321)
(121,320)(122,319)(123,318)(124,317)(125,316)(126,315)(127,314)(128,313)
(129,312)(130,311)(131,310)(132,309)(133,308)(134,307)(135,306)(136,305)
(137,304)(138,303)(139,302)(140,301)(141,300)(142,299)(143,298)(144,297)
(145,296)(146,295)(147,367)(148,366)(149,438)(150,437)(151,436)(152,435)
(153,434)(154,433)(155,432)(156,431)(157,430)(158,429)(159,428)(160,427)
(161,426)(162,425)(163,424)(164,423)(165,422)(166,421)(167,420)(168,419)
(169,418)(170,417)(171,416)(172,415)(173,414)(174,413)(175,412)(176,411)
(177,410)(178,409)(179,408)(180,407)(181,406)(182,405)(183,404)(184,403)
(185,402)(186,401)(187,400)(188,399)(189,398)(190,397)(191,396)(192,395)
(193,394)(194,393)(195,392)(196,391)(197,390)(198,389)(199,388)(200,387)
(201,386)(202,385)(203,384)(204,383)(205,382)(206,381)(207,380)(208,379)
(209,378)(210,377)(211,376)(212,375)(213,374)(214,373)(215,372)(216,371)
(217,370)(218,369)(219,368);;
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,
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*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*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*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*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(438)!( 74,147)( 75,148)( 76,149)( 77,150)( 78,151)( 79,152)( 80,153)
( 81,154)( 82,155)( 83,156)( 84,157)( 85,158)( 86,159)( 87,160)( 88,161)
( 89,162)( 90,163)( 91,164)( 92,165)( 93,166)( 94,167)( 95,168)( 96,169)
( 97,170)( 98,171)( 99,172)(100,173)(101,174)(102,175)(103,176)(104,177)
(105,178)(106,179)(107,180)(108,181)(109,182)(110,183)(111,184)(112,185)
(113,186)(114,187)(115,188)(116,189)(117,190)(118,191)(119,192)(120,193)
(121,194)(122,195)(123,196)(124,197)(125,198)(126,199)(127,200)(128,201)
(129,202)(130,203)(131,204)(132,205)(133,206)(134,207)(135,208)(136,209)
(137,210)(138,211)(139,212)(140,213)(141,214)(142,215)(143,216)(144,217)
(145,218)(146,219)(293,366)(294,367)(295,368)(296,369)(297,370)(298,371)
(299,372)(300,373)(301,374)(302,375)(303,376)(304,377)(305,378)(306,379)
(307,380)(308,381)(309,382)(310,383)(311,384)(312,385)(313,386)(314,387)
(315,388)(316,389)(317,390)(318,391)(319,392)(320,393)(321,394)(322,395)
(323,396)(324,397)(325,398)(326,399)(327,400)(328,401)(329,402)(330,403)
(331,404)(332,405)(333,406)(334,407)(335,408)(336,409)(337,410)(338,411)
(339,412)(340,413)(341,414)(342,415)(343,416)(344,417)(345,418)(346,419)
(347,420)(348,421)(349,422)(350,423)(351,424)(352,425)(353,426)(354,427)
(355,428)(356,429)(357,430)(358,431)(359,432)(360,433)(361,434)(362,435)
(363,436)(364,437)(365,438);
s1 := Sym(438)!( 1, 74)( 2,146)( 3,145)( 4,144)( 5,143)( 6,142)( 7,141)
( 8,140)( 9,139)( 10,138)( 11,137)( 12,136)( 13,135)( 14,134)( 15,133)
( 16,132)( 17,131)( 18,130)( 19,129)( 20,128)( 21,127)( 22,126)( 23,125)
( 24,124)( 25,123)( 26,122)( 27,121)( 28,120)( 29,119)( 30,118)( 31,117)
( 32,116)( 33,115)( 34,114)( 35,113)( 36,112)( 37,111)( 38,110)( 39,109)
( 40,108)( 41,107)( 42,106)( 43,105)( 44,104)( 45,103)( 46,102)( 47,101)
( 48,100)( 49, 99)( 50, 98)( 51, 97)( 52, 96)( 53, 95)( 54, 94)( 55, 93)
( 56, 92)( 57, 91)( 58, 90)( 59, 89)( 60, 88)( 61, 87)( 62, 86)( 63, 85)
( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)
( 72, 76)( 73, 75)(148,219)(149,218)(150,217)(151,216)(152,215)(153,214)
(154,213)(155,212)(156,211)(157,210)(158,209)(159,208)(160,207)(161,206)
(162,205)(163,204)(164,203)(165,202)(166,201)(167,200)(168,199)(169,198)
(170,197)(171,196)(172,195)(173,194)(174,193)(175,192)(176,191)(177,190)
(178,189)(179,188)(180,187)(181,186)(182,185)(183,184)(220,293)(221,365)
(222,364)(223,363)(224,362)(225,361)(226,360)(227,359)(228,358)(229,357)
(230,356)(231,355)(232,354)(233,353)(234,352)(235,351)(236,350)(237,349)
(238,348)(239,347)(240,346)(241,345)(242,344)(243,343)(244,342)(245,341)
(246,340)(247,339)(248,338)(249,337)(250,336)(251,335)(252,334)(253,333)
(254,332)(255,331)(256,330)(257,329)(258,328)(259,327)(260,326)(261,325)
(262,324)(263,323)(264,322)(265,321)(266,320)(267,319)(268,318)(269,317)
(270,316)(271,315)(272,314)(273,313)(274,312)(275,311)(276,310)(277,309)
(278,308)(279,307)(280,306)(281,305)(282,304)(283,303)(284,302)(285,301)
(286,300)(287,299)(288,298)(289,297)(290,296)(291,295)(292,294)(367,438)
(368,437)(369,436)(370,435)(371,434)(372,433)(373,432)(374,431)(375,430)
(376,429)(377,428)(378,427)(379,426)(380,425)(381,424)(382,423)(383,422)
(384,421)(385,420)(386,419)(387,418)(388,417)(389,416)(390,415)(391,414)
(392,413)(393,412)(394,411)(395,410)(396,409)(397,408)(398,407)(399,406)
(400,405)(401,404)(402,403);
s2 := Sym(438)!( 1,221)( 2,220)( 3,292)( 4,291)( 5,290)( 6,289)( 7,288)
( 8,287)( 9,286)( 10,285)( 11,284)( 12,283)( 13,282)( 14,281)( 15,280)
( 16,279)( 17,278)( 18,277)( 19,276)( 20,275)( 21,274)( 22,273)( 23,272)
( 24,271)( 25,270)( 26,269)( 27,268)( 28,267)( 29,266)( 30,265)( 31,264)
( 32,263)( 33,262)( 34,261)( 35,260)( 36,259)( 37,258)( 38,257)( 39,256)
( 40,255)( 41,254)( 42,253)( 43,252)( 44,251)( 45,250)( 46,249)( 47,248)
( 48,247)( 49,246)( 50,245)( 51,244)( 52,243)( 53,242)( 54,241)( 55,240)
( 56,239)( 57,238)( 58,237)( 59,236)( 60,235)( 61,234)( 62,233)( 63,232)
( 64,231)( 65,230)( 66,229)( 67,228)( 68,227)( 69,226)( 70,225)( 71,224)
( 72,223)( 73,222)( 74,294)( 75,293)( 76,365)( 77,364)( 78,363)( 79,362)
( 80,361)( 81,360)( 82,359)( 83,358)( 84,357)( 85,356)( 86,355)( 87,354)
( 88,353)( 89,352)( 90,351)( 91,350)( 92,349)( 93,348)( 94,347)( 95,346)
( 96,345)( 97,344)( 98,343)( 99,342)(100,341)(101,340)(102,339)(103,338)
(104,337)(105,336)(106,335)(107,334)(108,333)(109,332)(110,331)(111,330)
(112,329)(113,328)(114,327)(115,326)(116,325)(117,324)(118,323)(119,322)
(120,321)(121,320)(122,319)(123,318)(124,317)(125,316)(126,315)(127,314)
(128,313)(129,312)(130,311)(131,310)(132,309)(133,308)(134,307)(135,306)
(136,305)(137,304)(138,303)(139,302)(140,301)(141,300)(142,299)(143,298)
(144,297)(145,296)(146,295)(147,367)(148,366)(149,438)(150,437)(151,436)
(152,435)(153,434)(154,433)(155,432)(156,431)(157,430)(158,429)(159,428)
(160,427)(161,426)(162,425)(163,424)(164,423)(165,422)(166,421)(167,420)
(168,419)(169,418)(170,417)(171,416)(172,415)(173,414)(174,413)(175,412)
(176,411)(177,410)(178,409)(179,408)(180,407)(181,406)(182,405)(183,404)
(184,403)(185,402)(186,401)(187,400)(188,399)(189,398)(190,397)(191,396)
(192,395)(193,394)(194,393)(195,392)(196,391)(197,390)(198,389)(199,388)
(200,387)(201,386)(202,385)(203,384)(204,383)(205,382)(206,381)(207,380)
(208,379)(209,378)(210,377)(211,376)(212,375)(213,374)(214,373)(215,372)
(216,371)(217,370)(218,369)(219,368);
poly := sub<Sym(438)|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,
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*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*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*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*s1*s2*s1*s2 >;
References : None.
to this polytope