Polytope of Type {10,80}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,80}*1600b
if this polytope has a name.
Group : SmallGroup(1600,2764)
Rank : 3
Schlafli Type : {10,80}
Number of vertices, edges, etc : 10, 400, 80
Order of s₀s₁s₂ : 80
Order of s₀s₁s₂s₁ : 10
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 : {10,40}*800b
   4-fold quotients : {10,20}*400b
   5-fold quotients : {2,80}*320
   8-fold quotients : {10,10}*200b
   10-fold quotients : {2,40}*160
   16-fold quotients : {10,5}*100
   20-fold quotients : {2,20}*80
   25-fold quotients : {2,16}*64
   40-fold quotients : {2,10}*40
   50-fold quotients : {2,8}*32
   80-fold quotients : {2,5}*20
   100-fold quotients : {2,4}*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)( 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);;
s1 := (  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 21)( 12, 25)( 13, 24)
( 14, 23)( 15, 22)( 17, 20)( 18, 19)( 26, 31)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 36, 46)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 42, 45)( 43, 44)
( 51, 81)( 52, 85)( 53, 84)( 54, 83)( 55, 82)( 56, 76)( 57, 80)( 58, 79)
( 59, 78)( 60, 77)( 61, 96)( 62,100)( 63, 99)( 64, 98)( 65, 97)( 66, 91)
( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 86)( 72, 90)( 73, 89)( 74, 88)
( 75, 87)(101,156)(102,160)(103,159)(104,158)(105,157)(106,151)(107,155)
(108,154)(109,153)(110,152)(111,171)(112,175)(113,174)(114,173)(115,172)
(116,166)(117,170)(118,169)(119,168)(120,167)(121,161)(122,165)(123,164)
(124,163)(125,162)(126,181)(127,185)(128,184)(129,183)(130,182)(131,176)
(132,180)(133,179)(134,178)(135,177)(136,196)(137,200)(138,199)(139,198)
(140,197)(141,191)(142,195)(143,194)(144,193)(145,192)(146,186)(147,190)
(148,189)(149,188)(150,187)(201,306)(202,310)(203,309)(204,308)(205,307)
(206,301)(207,305)(208,304)(209,303)(210,302)(211,321)(212,325)(213,324)
(214,323)(215,322)(216,316)(217,320)(218,319)(219,318)(220,317)(221,311)
(222,315)(223,314)(224,313)(225,312)(226,331)(227,335)(228,334)(229,333)
(230,332)(231,326)(232,330)(233,329)(234,328)(235,327)(236,346)(237,350)
(238,349)(239,348)(240,347)(241,341)(242,345)(243,344)(244,343)(245,342)
(246,336)(247,340)(248,339)(249,338)(250,337)(251,381)(252,385)(253,384)
(254,383)(255,382)(256,376)(257,380)(258,379)(259,378)(260,377)(261,396)
(262,400)(263,399)(264,398)(265,397)(266,391)(267,395)(268,394)(269,393)
(270,392)(271,386)(272,390)(273,389)(274,388)(275,387)(276,356)(277,360)
(278,359)(279,358)(280,357)(281,351)(282,355)(283,354)(284,353)(285,352)
(286,371)(287,375)(288,374)(289,373)(290,372)(291,366)(292,370)(293,369)
(294,368)(295,367)(296,361)(297,365)(298,364)(299,363)(300,362);;
s2 := (  1,202)(  2,201)(  3,205)(  4,204)(  5,203)(  6,222)(  7,221)(  8,225)
(  9,224)( 10,223)( 11,217)( 12,216)( 13,220)( 14,219)( 15,218)( 16,212)
( 17,211)( 18,215)( 19,214)( 20,213)( 21,207)( 22,206)( 23,210)( 24,209)
( 25,208)( 26,227)( 27,226)( 28,230)( 29,229)( 30,228)( 31,247)( 32,246)
( 33,250)( 34,249)( 35,248)( 36,242)( 37,241)( 38,245)( 39,244)( 40,243)
( 41,237)( 42,236)( 43,240)( 44,239)( 45,238)( 46,232)( 47,231)( 48,235)
( 49,234)( 50,233)( 51,277)( 52,276)( 53,280)( 54,279)( 55,278)( 56,297)
( 57,296)( 58,300)( 59,299)( 60,298)( 61,292)( 62,291)( 63,295)( 64,294)
( 65,293)( 66,287)( 67,286)( 68,290)( 69,289)( 70,288)( 71,282)( 72,281)
( 73,285)( 74,284)( 75,283)( 76,252)( 77,251)( 78,255)( 79,254)( 80,253)
( 81,272)( 82,271)( 83,275)( 84,274)( 85,273)( 86,267)( 87,266)( 88,270)
( 89,269)( 90,268)( 91,262)( 92,261)( 93,265)( 94,264)( 95,263)( 96,257)
( 97,256)( 98,260)( 99,259)(100,258)(101,352)(102,351)(103,355)(104,354)
(105,353)(106,372)(107,371)(108,375)(109,374)(110,373)(111,367)(112,366)
(113,370)(114,369)(115,368)(116,362)(117,361)(118,365)(119,364)(120,363)
(121,357)(122,356)(123,360)(124,359)(125,358)(126,377)(127,376)(128,380)
(129,379)(130,378)(131,397)(132,396)(133,400)(134,399)(135,398)(136,392)
(137,391)(138,395)(139,394)(140,393)(141,387)(142,386)(143,390)(144,389)
(145,388)(146,382)(147,381)(148,385)(149,384)(150,383)(151,302)(152,301)
(153,305)(154,304)(155,303)(156,322)(157,321)(158,325)(159,324)(160,323)
(161,317)(162,316)(163,320)(164,319)(165,318)(166,312)(167,311)(168,315)
(169,314)(170,313)(171,307)(172,306)(173,310)(174,309)(175,308)(176,327)
(177,326)(178,330)(179,329)(180,328)(181,347)(182,346)(183,350)(184,349)
(185,348)(186,342)(187,341)(188,345)(189,344)(190,343)(191,337)(192,336)
(193,340)(194,339)(195,338)(196,332)(197,331)(198,335)(199,334)(200,333);;
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*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(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);
s1 := Sym(400)!(  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 21)( 12, 25)
( 13, 24)( 14, 23)( 15, 22)( 17, 20)( 18, 19)( 26, 31)( 27, 35)( 28, 34)
( 29, 33)( 30, 32)( 36, 46)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 42, 45)
( 43, 44)( 51, 81)( 52, 85)( 53, 84)( 54, 83)( 55, 82)( 56, 76)( 57, 80)
( 58, 79)( 59, 78)( 60, 77)( 61, 96)( 62,100)( 63, 99)( 64, 98)( 65, 97)
( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 86)( 72, 90)( 73, 89)
( 74, 88)( 75, 87)(101,156)(102,160)(103,159)(104,158)(105,157)(106,151)
(107,155)(108,154)(109,153)(110,152)(111,171)(112,175)(113,174)(114,173)
(115,172)(116,166)(117,170)(118,169)(119,168)(120,167)(121,161)(122,165)
(123,164)(124,163)(125,162)(126,181)(127,185)(128,184)(129,183)(130,182)
(131,176)(132,180)(133,179)(134,178)(135,177)(136,196)(137,200)(138,199)
(139,198)(140,197)(141,191)(142,195)(143,194)(144,193)(145,192)(146,186)
(147,190)(148,189)(149,188)(150,187)(201,306)(202,310)(203,309)(204,308)
(205,307)(206,301)(207,305)(208,304)(209,303)(210,302)(211,321)(212,325)
(213,324)(214,323)(215,322)(216,316)(217,320)(218,319)(219,318)(220,317)
(221,311)(222,315)(223,314)(224,313)(225,312)(226,331)(227,335)(228,334)
(229,333)(230,332)(231,326)(232,330)(233,329)(234,328)(235,327)(236,346)
(237,350)(238,349)(239,348)(240,347)(241,341)(242,345)(243,344)(244,343)
(245,342)(246,336)(247,340)(248,339)(249,338)(250,337)(251,381)(252,385)
(253,384)(254,383)(255,382)(256,376)(257,380)(258,379)(259,378)(260,377)
(261,396)(262,400)(263,399)(264,398)(265,397)(266,391)(267,395)(268,394)
(269,393)(270,392)(271,386)(272,390)(273,389)(274,388)(275,387)(276,356)
(277,360)(278,359)(279,358)(280,357)(281,351)(282,355)(283,354)(284,353)
(285,352)(286,371)(287,375)(288,374)(289,373)(290,372)(291,366)(292,370)
(293,369)(294,368)(295,367)(296,361)(297,365)(298,364)(299,363)(300,362);
s2 := Sym(400)!(  1,202)(  2,201)(  3,205)(  4,204)(  5,203)(  6,222)(  7,221)
(  8,225)(  9,224)( 10,223)( 11,217)( 12,216)( 13,220)( 14,219)( 15,218)
( 16,212)( 17,211)( 18,215)( 19,214)( 20,213)( 21,207)( 22,206)( 23,210)
( 24,209)( 25,208)( 26,227)( 27,226)( 28,230)( 29,229)( 30,228)( 31,247)
( 32,246)( 33,250)( 34,249)( 35,248)( 36,242)( 37,241)( 38,245)( 39,244)
( 40,243)( 41,237)( 42,236)( 43,240)( 44,239)( 45,238)( 46,232)( 47,231)
( 48,235)( 49,234)( 50,233)( 51,277)( 52,276)( 53,280)( 54,279)( 55,278)
( 56,297)( 57,296)( 58,300)( 59,299)( 60,298)( 61,292)( 62,291)( 63,295)
( 64,294)( 65,293)( 66,287)( 67,286)( 68,290)( 69,289)( 70,288)( 71,282)
( 72,281)( 73,285)( 74,284)( 75,283)( 76,252)( 77,251)( 78,255)( 79,254)
( 80,253)( 81,272)( 82,271)( 83,275)( 84,274)( 85,273)( 86,267)( 87,266)
( 88,270)( 89,269)( 90,268)( 91,262)( 92,261)( 93,265)( 94,264)( 95,263)
( 96,257)( 97,256)( 98,260)( 99,259)(100,258)(101,352)(102,351)(103,355)
(104,354)(105,353)(106,372)(107,371)(108,375)(109,374)(110,373)(111,367)
(112,366)(113,370)(114,369)(115,368)(116,362)(117,361)(118,365)(119,364)
(120,363)(121,357)(122,356)(123,360)(124,359)(125,358)(126,377)(127,376)
(128,380)(129,379)(130,378)(131,397)(132,396)(133,400)(134,399)(135,398)
(136,392)(137,391)(138,395)(139,394)(140,393)(141,387)(142,386)(143,390)
(144,389)(145,388)(146,382)(147,381)(148,385)(149,384)(150,383)(151,302)
(152,301)(153,305)(154,304)(155,303)(156,322)(157,321)(158,325)(159,324)
(160,323)(161,317)(162,316)(163,320)(164,319)(165,318)(166,312)(167,311)
(168,315)(169,314)(170,313)(171,307)(172,306)(173,310)(174,309)(175,308)
(176,327)(177,326)(178,330)(179,329)(180,328)(181,347)(182,346)(183,350)
(184,349)(185,348)(186,342)(187,341)(188,345)(189,344)(190,343)(191,337)
(192,336)(193,340)(194,339)(195,338)(196,332)(197,331)(198,335)(199,334)
(200,333);
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*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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