Polytope of Type {10,80}

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