Polytope of Type {80,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {80,10}*1600b
if this polytope has a name.
Group : SmallGroup(1600,2764)
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
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}*800b
   4-fold quotients : {20,10}*400b
   5-fold quotients : {80,2}*320
   8-fold quotients : {10,10}*200c
   10-fold quotients : {40,2}*160
   16-fold quotients : {5,10}*100
   20-fold quotients : {20,2}*80
   25-fold quotients : {16,2}*64
   40-fold quotients : {10,2}*40
   50-fold quotients : {8,2}*32
   80-fold quotients : {5,2}*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 := (  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)
( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)
( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56, 96)( 57,100)( 58, 99)
( 59, 98)( 60, 97)( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)( 66, 86)
( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 81)( 72, 85)( 73, 84)( 74, 83)
( 75, 82)(101,151)(102,155)(103,154)(104,153)(105,152)(106,171)(107,175)
(108,174)(109,173)(110,172)(111,166)(112,170)(113,169)(114,168)(115,167)
(116,161)(117,165)(118,164)(119,163)(120,162)(121,156)(122,160)(123,159)
(124,158)(125,157)(126,176)(127,180)(128,179)(129,178)(130,177)(131,196)
(132,200)(133,199)(134,198)(135,197)(136,191)(137,195)(138,194)(139,193)
(140,192)(141,186)(142,190)(143,189)(144,188)(145,187)(146,181)(147,185)
(148,184)(149,183)(150,182)(201,301)(202,305)(203,304)(204,303)(205,302)
(206,321)(207,325)(208,324)(209,323)(210,322)(211,316)(212,320)(213,319)
(214,318)(215,317)(216,311)(217,315)(218,314)(219,313)(220,312)(221,306)
(222,310)(223,309)(224,308)(225,307)(226,326)(227,330)(228,329)(229,328)
(230,327)(231,346)(232,350)(233,349)(234,348)(235,347)(236,341)(237,345)
(238,344)(239,343)(240,342)(241,336)(242,340)(243,339)(244,338)(245,337)
(246,331)(247,335)(248,334)(249,333)(250,332)(251,376)(252,380)(253,379)
(254,378)(255,377)(256,396)(257,400)(258,399)(259,398)(260,397)(261,391)
(262,395)(263,394)(264,393)(265,392)(266,386)(267,390)(268,389)(269,388)
(270,387)(271,381)(272,385)(273,384)(274,383)(275,382)(276,351)(277,355)
(278,354)(279,353)(280,352)(281,371)(282,375)(283,374)(284,373)(285,372)
(286,366)(287,370)(288,369)(289,368)(290,367)(291,361)(292,365)(293,364)
(294,363)(295,362)(296,356)(297,360)(298,359)(299,358)(300,357);;
s1 := (  1,207)(  2,206)(  3,210)(  4,209)(  5,208)(  6,202)(  7,201)(  8,205)
(  9,204)( 10,203)( 11,222)( 12,221)( 13,225)( 14,224)( 15,223)( 16,217)
( 17,216)( 18,220)( 19,219)( 20,218)( 21,212)( 22,211)( 23,215)( 24,214)
( 25,213)( 26,232)( 27,231)( 28,235)( 29,234)( 30,233)( 31,227)( 32,226)
( 33,230)( 34,229)( 35,228)( 36,247)( 37,246)( 38,250)( 39,249)( 40,248)
( 41,242)( 42,241)( 43,245)( 44,244)( 45,243)( 46,237)( 47,236)( 48,240)
( 49,239)( 50,238)( 51,282)( 52,281)( 53,285)( 54,284)( 55,283)( 56,277)
( 57,276)( 58,280)( 59,279)( 60,278)( 61,297)( 62,296)( 63,300)( 64,299)
( 65,298)( 66,292)( 67,291)( 68,295)( 69,294)( 70,293)( 71,287)( 72,286)
( 73,290)( 74,289)( 75,288)( 76,257)( 77,256)( 78,260)( 79,259)( 80,258)
( 81,252)( 82,251)( 83,255)( 84,254)( 85,253)( 86,272)( 87,271)( 88,275)
( 89,274)( 90,273)( 91,267)( 92,266)( 93,270)( 94,269)( 95,268)( 96,262)
( 97,261)( 98,265)( 99,264)(100,263)(101,357)(102,356)(103,360)(104,359)
(105,358)(106,352)(107,351)(108,355)(109,354)(110,353)(111,372)(112,371)
(113,375)(114,374)(115,373)(116,367)(117,366)(118,370)(119,369)(120,368)
(121,362)(122,361)(123,365)(124,364)(125,363)(126,382)(127,381)(128,385)
(129,384)(130,383)(131,377)(132,376)(133,380)(134,379)(135,378)(136,397)
(137,396)(138,400)(139,399)(140,398)(141,392)(142,391)(143,395)(144,394)
(145,393)(146,387)(147,386)(148,390)(149,389)(150,388)(151,307)(152,306)
(153,310)(154,309)(155,308)(156,302)(157,301)(158,305)(159,304)(160,303)
(161,322)(162,321)(163,325)(164,324)(165,323)(166,317)(167,316)(168,320)
(169,319)(170,318)(171,312)(172,311)(173,315)(174,314)(175,313)(176,332)
(177,331)(178,335)(179,334)(180,333)(181,327)(182,326)(183,330)(184,329)
(185,328)(186,347)(187,346)(188,350)(189,349)(190,348)(191,342)(192,341)
(193,345)(194,344)(195,343)(196,337)(197,336)(198,340)(199,339)(200,338);;
s2 := (  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)( 56, 71)( 57, 72)( 58, 73)( 59, 74)
( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)
( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)
(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)
(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)
(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)(159,174)
(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)(182,197)
(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)(190,195)
(206,221)(207,222)(208,223)(209,224)(210,225)(211,216)(212,217)(213,218)
(214,219)(215,220)(231,246)(232,247)(233,248)(234,249)(235,250)(236,241)
(237,242)(238,243)(239,244)(240,245)(256,271)(257,272)(258,273)(259,274)
(260,275)(261,266)(262,267)(263,268)(264,269)(265,270)(281,296)(282,297)
(283,298)(284,299)(285,300)(286,291)(287,292)(288,293)(289,294)(290,295)
(306,321)(307,322)(308,323)(309,324)(310,325)(311,316)(312,317)(313,318)
(314,319)(315,320)(331,346)(332,347)(333,348)(334,349)(335,350)(336,341)
(337,342)(338,343)(339,344)(340,345)(356,371)(357,372)(358,373)(359,374)
(360,375)(361,366)(362,367)(363,368)(364,369)(365,370)(381,396)(382,397)
(383,398)(384,399)(385,400)(386,391)(387,392)(388,393)(389,394)(390,395);;
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*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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*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*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(400)!(  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)
( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)
( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)
( 40, 42)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56, 96)( 57,100)
( 58, 99)( 59, 98)( 60, 97)( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)
( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 81)( 72, 85)( 73, 84)
( 74, 83)( 75, 82)(101,151)(102,155)(103,154)(104,153)(105,152)(106,171)
(107,175)(108,174)(109,173)(110,172)(111,166)(112,170)(113,169)(114,168)
(115,167)(116,161)(117,165)(118,164)(119,163)(120,162)(121,156)(122,160)
(123,159)(124,158)(125,157)(126,176)(127,180)(128,179)(129,178)(130,177)
(131,196)(132,200)(133,199)(134,198)(135,197)(136,191)(137,195)(138,194)
(139,193)(140,192)(141,186)(142,190)(143,189)(144,188)(145,187)(146,181)
(147,185)(148,184)(149,183)(150,182)(201,301)(202,305)(203,304)(204,303)
(205,302)(206,321)(207,325)(208,324)(209,323)(210,322)(211,316)(212,320)
(213,319)(214,318)(215,317)(216,311)(217,315)(218,314)(219,313)(220,312)
(221,306)(222,310)(223,309)(224,308)(225,307)(226,326)(227,330)(228,329)
(229,328)(230,327)(231,346)(232,350)(233,349)(234,348)(235,347)(236,341)
(237,345)(238,344)(239,343)(240,342)(241,336)(242,340)(243,339)(244,338)
(245,337)(246,331)(247,335)(248,334)(249,333)(250,332)(251,376)(252,380)
(253,379)(254,378)(255,377)(256,396)(257,400)(258,399)(259,398)(260,397)
(261,391)(262,395)(263,394)(264,393)(265,392)(266,386)(267,390)(268,389)
(269,388)(270,387)(271,381)(272,385)(273,384)(274,383)(275,382)(276,351)
(277,355)(278,354)(279,353)(280,352)(281,371)(282,375)(283,374)(284,373)
(285,372)(286,366)(287,370)(288,369)(289,368)(290,367)(291,361)(292,365)
(293,364)(294,363)(295,362)(296,356)(297,360)(298,359)(299,358)(300,357);
s1 := Sym(400)!(  1,207)(  2,206)(  3,210)(  4,209)(  5,208)(  6,202)(  7,201)
(  8,205)(  9,204)( 10,203)( 11,222)( 12,221)( 13,225)( 14,224)( 15,223)
( 16,217)( 17,216)( 18,220)( 19,219)( 20,218)( 21,212)( 22,211)( 23,215)
( 24,214)( 25,213)( 26,232)( 27,231)( 28,235)( 29,234)( 30,233)( 31,227)
( 32,226)( 33,230)( 34,229)( 35,228)( 36,247)( 37,246)( 38,250)( 39,249)
( 40,248)( 41,242)( 42,241)( 43,245)( 44,244)( 45,243)( 46,237)( 47,236)
( 48,240)( 49,239)( 50,238)( 51,282)( 52,281)( 53,285)( 54,284)( 55,283)
( 56,277)( 57,276)( 58,280)( 59,279)( 60,278)( 61,297)( 62,296)( 63,300)
( 64,299)( 65,298)( 66,292)( 67,291)( 68,295)( 69,294)( 70,293)( 71,287)
( 72,286)( 73,290)( 74,289)( 75,288)( 76,257)( 77,256)( 78,260)( 79,259)
( 80,258)( 81,252)( 82,251)( 83,255)( 84,254)( 85,253)( 86,272)( 87,271)
( 88,275)( 89,274)( 90,273)( 91,267)( 92,266)( 93,270)( 94,269)( 95,268)
( 96,262)( 97,261)( 98,265)( 99,264)(100,263)(101,357)(102,356)(103,360)
(104,359)(105,358)(106,352)(107,351)(108,355)(109,354)(110,353)(111,372)
(112,371)(113,375)(114,374)(115,373)(116,367)(117,366)(118,370)(119,369)
(120,368)(121,362)(122,361)(123,365)(124,364)(125,363)(126,382)(127,381)
(128,385)(129,384)(130,383)(131,377)(132,376)(133,380)(134,379)(135,378)
(136,397)(137,396)(138,400)(139,399)(140,398)(141,392)(142,391)(143,395)
(144,394)(145,393)(146,387)(147,386)(148,390)(149,389)(150,388)(151,307)
(152,306)(153,310)(154,309)(155,308)(156,302)(157,301)(158,305)(159,304)
(160,303)(161,322)(162,321)(163,325)(164,324)(165,323)(166,317)(167,316)
(168,320)(169,319)(170,318)(171,312)(172,311)(173,315)(174,314)(175,313)
(176,332)(177,331)(178,335)(179,334)(180,333)(181,327)(182,326)(183,330)
(184,329)(185,328)(186,347)(187,346)(188,350)(189,349)(190,348)(191,342)
(192,341)(193,345)(194,344)(195,343)(196,337)(197,336)(198,340)(199,339)
(200,338);
s2 := 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)( 56, 71)( 57, 72)( 58, 73)
( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)
( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)
( 90, 95)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)
(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)
(136,141)(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)
(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)
(182,197)(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)
(190,195)(206,221)(207,222)(208,223)(209,224)(210,225)(211,216)(212,217)
(213,218)(214,219)(215,220)(231,246)(232,247)(233,248)(234,249)(235,250)
(236,241)(237,242)(238,243)(239,244)(240,245)(256,271)(257,272)(258,273)
(259,274)(260,275)(261,266)(262,267)(263,268)(264,269)(265,270)(281,296)
(282,297)(283,298)(284,299)(285,300)(286,291)(287,292)(288,293)(289,294)
(290,295)(306,321)(307,322)(308,323)(309,324)(310,325)(311,316)(312,317)
(313,318)(314,319)(315,320)(331,346)(332,347)(333,348)(334,349)(335,350)
(336,341)(337,342)(338,343)(339,344)(340,345)(356,371)(357,372)(358,373)
(359,374)(360,375)(361,366)(362,367)(363,368)(364,369)(365,370)(381,396)
(382,397)(383,398)(384,399)(385,400)(386,391)(387,392)(388,393)(389,394)
(390,395);
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*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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*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*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