Polytope of Type {10,80}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,80}*1600c
if this polytope has a name.
Group : SmallGroup(1600,3558)
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}*800c
   4-fold quotients : {10,20}*400c
   5-fold quotients : {10,16}*320
   8-fold quotients : {10,10}*200c
   10-fold quotients : {10,8}*160
   16-fold quotients : {5,10}*100
   20-fold quotients : {10,4}*80
   25-fold quotients : {2,16}*64
   40-fold quotients : {10,2}*40
   50-fold quotients : {2,8}*32
   80-fold quotients : {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 := (  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)
( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)
( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)
( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)
(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)
(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)(132,150)
(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)
(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)(161,166)
(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)(182,200)
(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)(190,192)
(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)(211,216)
(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)(232,250)
(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)(240,242)
(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)(261,266)
(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)(282,300)
(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)(290,292)
(302,305)(303,304)(306,321)(307,325)(308,324)(309,323)(310,322)(311,316)
(312,320)(313,319)(314,318)(315,317)(327,330)(328,329)(331,346)(332,350)
(333,349)(334,348)(335,347)(336,341)(337,345)(338,344)(339,343)(340,342)
(352,355)(353,354)(356,371)(357,375)(358,374)(359,373)(360,372)(361,366)
(362,370)(363,369)(364,368)(365,367)(377,380)(378,379)(381,396)(382,400)
(383,399)(384,398)(385,397)(386,391)(387,395)(388,394)(389,393)(390,392);;
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)( 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);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)
( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)
( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)
( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)
(111,116)(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)
(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)
(140,142)(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)
(161,166)(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)
(182,200)(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)
(190,192)(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)
(211,216)(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)
(232,250)(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)
(240,242)(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)
(261,266)(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)
(282,300)(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)
(290,292)(302,305)(303,304)(306,321)(307,325)(308,324)(309,323)(310,322)
(311,316)(312,320)(313,319)(314,318)(315,317)(327,330)(328,329)(331,346)
(332,350)(333,349)(334,348)(335,347)(336,341)(337,345)(338,344)(339,343)
(340,342)(352,355)(353,354)(356,371)(357,375)(358,374)(359,373)(360,372)
(361,366)(362,370)(363,369)(364,368)(365,367)(377,380)(378,379)(381,396)
(382,400)(383,399)(384,398)(385,397)(386,391)(387,395)(388,394)(389,393)
(390,392);
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)( 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);
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;

References : None.
to this polytope