Polytope of Type {80,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {80,10}*1600c
if this polytope has a name.
Group : SmallGroup(1600,3558)
Rank : 3
Schlafli Type : {80,10}
Number of vertices, edges, etc : 80, 400, 10
Order of s₀s₁s₂ : 80
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
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 : {40,10}*800c
   4-fold quotients : {20,10}*400c
   5-fold quotients : {16,10}*320
   8-fold quotients : {10,10}*200b
   10-fold quotients : {8,10}*160
   16-fold quotients : {10,5}*100
   20-fold quotients : {4,10}*80
   25-fold quotients : {16,2}*64
   40-fold quotients : {2,10}*40
   50-fold quotients : {8,2}*32
   80-fold quotients : {2,5}*20
   100-fold quotients : {4,2}*16
   200-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 76)( 52, 77)( 53, 78)( 54, 79)
( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)( 62, 92)
( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)
( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)(101,151)(102,152)(103,153)
(104,154)(105,155)(106,171)(107,172)(108,173)(109,174)(110,175)(111,166)
(112,167)(113,168)(114,169)(115,170)(116,161)(117,162)(118,163)(119,164)
(120,165)(121,156)(122,157)(123,158)(124,159)(125,160)(126,176)(127,177)
(128,178)(129,179)(130,180)(131,196)(132,197)(133,198)(134,199)(135,200)
(136,191)(137,192)(138,193)(139,194)(140,195)(141,186)(142,187)(143,188)
(144,189)(145,190)(146,181)(147,182)(148,183)(149,184)(150,185)(201,301)
(202,302)(203,303)(204,304)(205,305)(206,321)(207,322)(208,323)(209,324)
(210,325)(211,316)(212,317)(213,318)(214,319)(215,320)(216,311)(217,312)
(218,313)(219,314)(220,315)(221,306)(222,307)(223,308)(224,309)(225,310)
(226,326)(227,327)(228,328)(229,329)(230,330)(231,346)(232,347)(233,348)
(234,349)(235,350)(236,341)(237,342)(238,343)(239,344)(240,345)(241,336)
(242,337)(243,338)(244,339)(245,340)(246,331)(247,332)(248,333)(249,334)
(250,335)(251,376)(252,377)(253,378)(254,379)(255,380)(256,396)(257,397)
(258,398)(259,399)(260,400)(261,391)(262,392)(263,393)(264,394)(265,395)
(266,386)(267,387)(268,388)(269,389)(270,390)(271,381)(272,382)(273,383)
(274,384)(275,385)(276,351)(277,352)(278,353)(279,354)(280,355)(281,371)
(282,372)(283,373)(284,374)(285,375)(286,366)(287,367)(288,368)(289,369)
(290,370)(291,361)(292,362)(293,363)(294,364)(295,365)(296,356)(297,357)
(298,358)(299,359)(300,360);;
s1 := (  1,206)(  2,210)(  3,209)(  4,208)(  5,207)(  6,201)(  7,205)(  8,204)
(  9,203)( 10,202)( 11,221)( 12,225)( 13,224)( 14,223)( 15,222)( 16,216)
( 17,220)( 18,219)( 19,218)( 20,217)( 21,211)( 22,215)( 23,214)( 24,213)
( 25,212)( 26,231)( 27,235)( 28,234)( 29,233)( 30,232)( 31,226)( 32,230)
( 33,229)( 34,228)( 35,227)( 36,246)( 37,250)( 38,249)( 39,248)( 40,247)
( 41,241)( 42,245)( 43,244)( 44,243)( 45,242)( 46,236)( 47,240)( 48,239)
( 49,238)( 50,237)( 51,281)( 52,285)( 53,284)( 54,283)( 55,282)( 56,276)
( 57,280)( 58,279)( 59,278)( 60,277)( 61,296)( 62,300)( 63,299)( 64,298)
( 65,297)( 66,291)( 67,295)( 68,294)( 69,293)( 70,292)( 71,286)( 72,290)
( 73,289)( 74,288)( 75,287)( 76,256)( 77,260)( 78,259)( 79,258)( 80,257)
( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,271)( 87,275)( 88,274)
( 89,273)( 90,272)( 91,266)( 92,270)( 93,269)( 94,268)( 95,267)( 96,261)
( 97,265)( 98,264)( 99,263)(100,262)(101,356)(102,360)(103,359)(104,358)
(105,357)(106,351)(107,355)(108,354)(109,353)(110,352)(111,371)(112,375)
(113,374)(114,373)(115,372)(116,366)(117,370)(118,369)(119,368)(120,367)
(121,361)(122,365)(123,364)(124,363)(125,362)(126,381)(127,385)(128,384)
(129,383)(130,382)(131,376)(132,380)(133,379)(134,378)(135,377)(136,396)
(137,400)(138,399)(139,398)(140,397)(141,391)(142,395)(143,394)(144,393)
(145,392)(146,386)(147,390)(148,389)(149,388)(150,387)(151,306)(152,310)
(153,309)(154,308)(155,307)(156,301)(157,305)(158,304)(159,303)(160,302)
(161,321)(162,325)(163,324)(164,323)(165,322)(166,316)(167,320)(168,319)
(169,318)(170,317)(171,311)(172,315)(173,314)(174,313)(175,312)(176,331)
(177,335)(178,334)(179,333)(180,332)(181,326)(182,330)(183,329)(184,328)
(185,327)(186,346)(187,350)(188,349)(189,348)(190,347)(191,341)(192,345)
(193,344)(194,343)(195,342)(196,336)(197,340)(198,339)(199,338)(200,337);;
s2 := (  1,  2)(  3,  5)(  6, 22)(  7, 21)(  8, 25)(  9, 24)( 10, 23)( 11, 17)
( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 27)( 28, 30)( 31, 47)( 32, 46)
( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)( 40, 43)
( 51, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)( 61, 67)
( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76, 77)( 78, 80)( 81, 97)( 82, 96)
( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)( 90, 93)
(101,102)(103,105)(106,122)(107,121)(108,125)(109,124)(110,123)(111,117)
(112,116)(113,120)(114,119)(115,118)(126,127)(128,130)(131,147)(132,146)
(133,150)(134,149)(135,148)(136,142)(137,141)(138,145)(139,144)(140,143)
(151,152)(153,155)(156,172)(157,171)(158,175)(159,174)(160,173)(161,167)
(162,166)(163,170)(164,169)(165,168)(176,177)(178,180)(181,197)(182,196)
(183,200)(184,199)(185,198)(186,192)(187,191)(188,195)(189,194)(190,193)
(201,202)(203,205)(206,222)(207,221)(208,225)(209,224)(210,223)(211,217)
(212,216)(213,220)(214,219)(215,218)(226,227)(228,230)(231,247)(232,246)
(233,250)(234,249)(235,248)(236,242)(237,241)(238,245)(239,244)(240,243)
(251,252)(253,255)(256,272)(257,271)(258,275)(259,274)(260,273)(261,267)
(262,266)(263,270)(264,269)(265,268)(276,277)(278,280)(281,297)(282,296)
(283,300)(284,299)(285,298)(286,292)(287,291)(288,295)(289,294)(290,293)
(301,302)(303,305)(306,322)(307,321)(308,325)(309,324)(310,323)(311,317)
(312,316)(313,320)(314,319)(315,318)(326,327)(328,330)(331,347)(332,346)
(333,350)(334,349)(335,348)(336,342)(337,341)(338,345)(339,344)(340,343)
(351,352)(353,355)(356,372)(357,371)(358,375)(359,374)(360,373)(361,367)
(362,366)(363,370)(364,369)(365,368)(376,377)(378,380)(381,397)(382,396)
(383,400)(384,399)(385,398)(386,392)(387,391)(388,395)(389,394)(390,393);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(400)!(  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 76)( 52, 77)( 53, 78)
( 54, 79)( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)
( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)
( 70, 90)( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)(101,151)(102,152)
(103,153)(104,154)(105,155)(106,171)(107,172)(108,173)(109,174)(110,175)
(111,166)(112,167)(113,168)(114,169)(115,170)(116,161)(117,162)(118,163)
(119,164)(120,165)(121,156)(122,157)(123,158)(124,159)(125,160)(126,176)
(127,177)(128,178)(129,179)(130,180)(131,196)(132,197)(133,198)(134,199)
(135,200)(136,191)(137,192)(138,193)(139,194)(140,195)(141,186)(142,187)
(143,188)(144,189)(145,190)(146,181)(147,182)(148,183)(149,184)(150,185)
(201,301)(202,302)(203,303)(204,304)(205,305)(206,321)(207,322)(208,323)
(209,324)(210,325)(211,316)(212,317)(213,318)(214,319)(215,320)(216,311)
(217,312)(218,313)(219,314)(220,315)(221,306)(222,307)(223,308)(224,309)
(225,310)(226,326)(227,327)(228,328)(229,329)(230,330)(231,346)(232,347)
(233,348)(234,349)(235,350)(236,341)(237,342)(238,343)(239,344)(240,345)
(241,336)(242,337)(243,338)(244,339)(245,340)(246,331)(247,332)(248,333)
(249,334)(250,335)(251,376)(252,377)(253,378)(254,379)(255,380)(256,396)
(257,397)(258,398)(259,399)(260,400)(261,391)(262,392)(263,393)(264,394)
(265,395)(266,386)(267,387)(268,388)(269,389)(270,390)(271,381)(272,382)
(273,383)(274,384)(275,385)(276,351)(277,352)(278,353)(279,354)(280,355)
(281,371)(282,372)(283,373)(284,374)(285,375)(286,366)(287,367)(288,368)
(289,369)(290,370)(291,361)(292,362)(293,363)(294,364)(295,365)(296,356)
(297,357)(298,358)(299,359)(300,360);
s1 := Sym(400)!(  1,206)(  2,210)(  3,209)(  4,208)(  5,207)(  6,201)(  7,205)
(  8,204)(  9,203)( 10,202)( 11,221)( 12,225)( 13,224)( 14,223)( 15,222)
( 16,216)( 17,220)( 18,219)( 19,218)( 20,217)( 21,211)( 22,215)( 23,214)
( 24,213)( 25,212)( 26,231)( 27,235)( 28,234)( 29,233)( 30,232)( 31,226)
( 32,230)( 33,229)( 34,228)( 35,227)( 36,246)( 37,250)( 38,249)( 39,248)
( 40,247)( 41,241)( 42,245)( 43,244)( 44,243)( 45,242)( 46,236)( 47,240)
( 48,239)( 49,238)( 50,237)( 51,281)( 52,285)( 53,284)( 54,283)( 55,282)
( 56,276)( 57,280)( 58,279)( 59,278)( 60,277)( 61,296)( 62,300)( 63,299)
( 64,298)( 65,297)( 66,291)( 67,295)( 68,294)( 69,293)( 70,292)( 71,286)
( 72,290)( 73,289)( 74,288)( 75,287)( 76,256)( 77,260)( 78,259)( 79,258)
( 80,257)( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,271)( 87,275)
( 88,274)( 89,273)( 90,272)( 91,266)( 92,270)( 93,269)( 94,268)( 95,267)
( 96,261)( 97,265)( 98,264)( 99,263)(100,262)(101,356)(102,360)(103,359)
(104,358)(105,357)(106,351)(107,355)(108,354)(109,353)(110,352)(111,371)
(112,375)(113,374)(114,373)(115,372)(116,366)(117,370)(118,369)(119,368)
(120,367)(121,361)(122,365)(123,364)(124,363)(125,362)(126,381)(127,385)
(128,384)(129,383)(130,382)(131,376)(132,380)(133,379)(134,378)(135,377)
(136,396)(137,400)(138,399)(139,398)(140,397)(141,391)(142,395)(143,394)
(144,393)(145,392)(146,386)(147,390)(148,389)(149,388)(150,387)(151,306)
(152,310)(153,309)(154,308)(155,307)(156,301)(157,305)(158,304)(159,303)
(160,302)(161,321)(162,325)(163,324)(164,323)(165,322)(166,316)(167,320)
(168,319)(169,318)(170,317)(171,311)(172,315)(173,314)(174,313)(175,312)
(176,331)(177,335)(178,334)(179,333)(180,332)(181,326)(182,330)(183,329)
(184,328)(185,327)(186,346)(187,350)(188,349)(189,348)(190,347)(191,341)
(192,345)(193,344)(194,343)(195,342)(196,336)(197,340)(198,339)(199,338)
(200,337);
s2 := Sym(400)!(  1,  2)(  3,  5)(  6, 22)(  7, 21)(  8, 25)(  9, 24)( 10, 23)
( 11, 17)( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 27)( 28, 30)( 31, 47)
( 32, 46)( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)
( 40, 43)( 51, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)
( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76, 77)( 78, 80)( 81, 97)
( 82, 96)( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)
( 90, 93)(101,102)(103,105)(106,122)(107,121)(108,125)(109,124)(110,123)
(111,117)(112,116)(113,120)(114,119)(115,118)(126,127)(128,130)(131,147)
(132,146)(133,150)(134,149)(135,148)(136,142)(137,141)(138,145)(139,144)
(140,143)(151,152)(153,155)(156,172)(157,171)(158,175)(159,174)(160,173)
(161,167)(162,166)(163,170)(164,169)(165,168)(176,177)(178,180)(181,197)
(182,196)(183,200)(184,199)(185,198)(186,192)(187,191)(188,195)(189,194)
(190,193)(201,202)(203,205)(206,222)(207,221)(208,225)(209,224)(210,223)
(211,217)(212,216)(213,220)(214,219)(215,218)(226,227)(228,230)(231,247)
(232,246)(233,250)(234,249)(235,248)(236,242)(237,241)(238,245)(239,244)
(240,243)(251,252)(253,255)(256,272)(257,271)(258,275)(259,274)(260,273)
(261,267)(262,266)(263,270)(264,269)(265,268)(276,277)(278,280)(281,297)
(282,296)(283,300)(284,299)(285,298)(286,292)(287,291)(288,295)(289,294)
(290,293)(301,302)(303,305)(306,322)(307,321)(308,325)(309,324)(310,323)
(311,317)(312,316)(313,320)(314,319)(315,318)(326,327)(328,330)(331,347)
(332,346)(333,350)(334,349)(335,348)(336,342)(337,341)(338,345)(339,344)
(340,343)(351,352)(353,355)(356,372)(357,371)(358,375)(359,374)(360,373)
(361,367)(362,366)(363,370)(364,369)(365,368)(376,377)(378,380)(381,397)
(382,396)(383,400)(384,399)(385,398)(386,392)(387,391)(388,395)(389,394)
(390,393);
poly := sub<Sym(400)|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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope