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Polytope of Type {5,10,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,10,16}*1600
if this polytope has a name.
Group : SmallGroup(1600,3558)
Rank : 4
Schlafli Type : {5,10,16}
Number of vertices, edges, etc : 5, 25, 80, 16
Order of s0s1s2s3 : 80
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   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 : {5,10,8}*800
   4-fold quotients : {5,10,4}*400
   5-fold quotients : {5,2,16}*320
   8-fold quotients : {5,10,2}*200
   10-fold quotients : {5,2,8}*160
   20-fold quotients : {5,2,4}*80
   40-fold quotients : {5,2,2}*40
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,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 22)( 12, 21)( 13, 25)
( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 32)( 27, 31)( 28, 35)( 29, 34)
( 30, 33)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 42)( 43, 45)
( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)( 63, 75)
( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 82)( 77, 81)( 78, 85)( 79, 84)
( 80, 83)( 86, 97)( 87, 96)( 88,100)( 89, 99)( 90, 98)( 91, 92)( 93, 95)
(101,107)(102,106)(103,110)(104,109)(105,108)(111,122)(112,121)(113,125)
(114,124)(115,123)(116,117)(118,120)(126,132)(127,131)(128,135)(129,134)
(130,133)(136,147)(137,146)(138,150)(139,149)(140,148)(141,142)(143,145)
(151,157)(152,156)(153,160)(154,159)(155,158)(161,172)(162,171)(163,175)
(164,174)(165,173)(166,167)(168,170)(176,182)(177,181)(178,185)(179,184)
(180,183)(186,197)(187,196)(188,200)(189,199)(190,198)(191,192)(193,195)
(201,207)(202,206)(203,210)(204,209)(205,208)(211,222)(212,221)(213,225)
(214,224)(215,223)(216,217)(218,220)(226,232)(227,231)(228,235)(229,234)
(230,233)(236,247)(237,246)(238,250)(239,249)(240,248)(241,242)(243,245)
(251,257)(252,256)(253,260)(254,259)(255,258)(261,272)(262,271)(263,275)
(264,274)(265,273)(266,267)(268,270)(276,282)(277,281)(278,285)(279,284)
(280,283)(286,297)(287,296)(288,300)(289,299)(290,298)(291,292)(293,295)
(301,307)(302,306)(303,310)(304,309)(305,308)(311,322)(312,321)(313,325)
(314,324)(315,323)(316,317)(318,320)(326,332)(327,331)(328,335)(329,334)
(330,333)(336,347)(337,346)(338,350)(339,349)(340,348)(341,342)(343,345)
(351,357)(352,356)(353,360)(354,359)(355,358)(361,372)(362,371)(363,375)
(364,374)(365,373)(366,367)(368,370)(376,382)(377,381)(378,385)(379,384)
(380,383)(386,397)(387,396)(388,400)(389,399)(390,398)(391,392)(393,395);;
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);;
s3 := (  1,201)(  2,202)(  3,203)(  4,204)(  5,205)(  6,206)(  7,207)(  8,208)
(  9,209)( 10,210)( 11,211)( 12,212)( 13,213)( 14,214)( 15,215)( 16,216)
( 17,217)( 18,218)( 19,219)( 20,220)( 21,221)( 22,222)( 23,223)( 24,224)
( 25,225)( 26,226)( 27,227)( 28,228)( 29,229)( 30,230)( 31,231)( 32,232)
( 33,233)( 34,234)( 35,235)( 36,236)( 37,237)( 38,238)( 39,239)( 40,240)
( 41,241)( 42,242)( 43,243)( 44,244)( 45,245)( 46,246)( 47,247)( 48,248)
( 49,249)( 50,250)( 51,276)( 52,277)( 53,278)( 54,279)( 55,280)( 56,281)
( 57,282)( 58,283)( 59,284)( 60,285)( 61,286)( 62,287)( 63,288)( 64,289)
( 65,290)( 66,291)( 67,292)( 68,293)( 69,294)( 70,295)( 71,296)( 72,297)
( 73,298)( 74,299)( 75,300)( 76,251)( 77,252)( 78,253)( 79,254)( 80,255)
( 81,256)( 82,257)( 83,258)( 84,259)( 85,260)( 86,261)( 87,262)( 88,263)
( 89,264)( 90,265)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)( 96,271)
( 97,272)( 98,273)( 99,274)(100,275)(101,351)(102,352)(103,353)(104,354)
(105,355)(106,356)(107,357)(108,358)(109,359)(110,360)(111,361)(112,362)
(113,363)(114,364)(115,365)(116,366)(117,367)(118,368)(119,369)(120,370)
(121,371)(122,372)(123,373)(124,374)(125,375)(126,376)(127,377)(128,378)
(129,379)(130,380)(131,381)(132,382)(133,383)(134,384)(135,385)(136,386)
(137,387)(138,388)(139,389)(140,390)(141,391)(142,392)(143,393)(144,394)
(145,395)(146,396)(147,397)(148,398)(149,399)(150,400)(151,301)(152,302)
(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)(160,310)
(161,311)(162,312)(163,313)(164,314)(165,315)(166,316)(167,317)(168,318)
(169,319)(170,320)(171,321)(172,322)(173,323)(174,324)(175,325)(176,326)
(177,327)(178,328)(179,329)(180,330)(181,331)(182,332)(183,333)(184,334)
(185,335)(186,336)(187,337)(188,338)(189,339)(190,340)(191,341)(192,342)
(193,343)(194,344)(195,345)(196,346)(197,347)(198,348)(199,349)(200,350);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 22)( 12, 21)
( 13, 25)( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 32)( 27, 31)( 28, 35)
( 29, 34)( 30, 33)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 42)
( 43, 45)( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)
( 63, 75)( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 82)( 77, 81)( 78, 85)
( 79, 84)( 80, 83)( 86, 97)( 87, 96)( 88,100)( 89, 99)( 90, 98)( 91, 92)
( 93, 95)(101,107)(102,106)(103,110)(104,109)(105,108)(111,122)(112,121)
(113,125)(114,124)(115,123)(116,117)(118,120)(126,132)(127,131)(128,135)
(129,134)(130,133)(136,147)(137,146)(138,150)(139,149)(140,148)(141,142)
(143,145)(151,157)(152,156)(153,160)(154,159)(155,158)(161,172)(162,171)
(163,175)(164,174)(165,173)(166,167)(168,170)(176,182)(177,181)(178,185)
(179,184)(180,183)(186,197)(187,196)(188,200)(189,199)(190,198)(191,192)
(193,195)(201,207)(202,206)(203,210)(204,209)(205,208)(211,222)(212,221)
(213,225)(214,224)(215,223)(216,217)(218,220)(226,232)(227,231)(228,235)
(229,234)(230,233)(236,247)(237,246)(238,250)(239,249)(240,248)(241,242)
(243,245)(251,257)(252,256)(253,260)(254,259)(255,258)(261,272)(262,271)
(263,275)(264,274)(265,273)(266,267)(268,270)(276,282)(277,281)(278,285)
(279,284)(280,283)(286,297)(287,296)(288,300)(289,299)(290,298)(291,292)
(293,295)(301,307)(302,306)(303,310)(304,309)(305,308)(311,322)(312,321)
(313,325)(314,324)(315,323)(316,317)(318,320)(326,332)(327,331)(328,335)
(329,334)(330,333)(336,347)(337,346)(338,350)(339,349)(340,348)(341,342)
(343,345)(351,357)(352,356)(353,360)(354,359)(355,358)(361,372)(362,371)
(363,375)(364,374)(365,373)(366,367)(368,370)(376,382)(377,381)(378,385)
(379,384)(380,383)(386,397)(387,396)(388,400)(389,399)(390,398)(391,392)
(393,395);
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);
s3 := Sym(400)!(  1,201)(  2,202)(  3,203)(  4,204)(  5,205)(  6,206)(  7,207)
(  8,208)(  9,209)( 10,210)( 11,211)( 12,212)( 13,213)( 14,214)( 15,215)
( 16,216)( 17,217)( 18,218)( 19,219)( 20,220)( 21,221)( 22,222)( 23,223)
( 24,224)( 25,225)( 26,226)( 27,227)( 28,228)( 29,229)( 30,230)( 31,231)
( 32,232)( 33,233)( 34,234)( 35,235)( 36,236)( 37,237)( 38,238)( 39,239)
( 40,240)( 41,241)( 42,242)( 43,243)( 44,244)( 45,245)( 46,246)( 47,247)
( 48,248)( 49,249)( 50,250)( 51,276)( 52,277)( 53,278)( 54,279)( 55,280)
( 56,281)( 57,282)( 58,283)( 59,284)( 60,285)( 61,286)( 62,287)( 63,288)
( 64,289)( 65,290)( 66,291)( 67,292)( 68,293)( 69,294)( 70,295)( 71,296)
( 72,297)( 73,298)( 74,299)( 75,300)( 76,251)( 77,252)( 78,253)( 79,254)
( 80,255)( 81,256)( 82,257)( 83,258)( 84,259)( 85,260)( 86,261)( 87,262)
( 88,263)( 89,264)( 90,265)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)
( 96,271)( 97,272)( 98,273)( 99,274)(100,275)(101,351)(102,352)(103,353)
(104,354)(105,355)(106,356)(107,357)(108,358)(109,359)(110,360)(111,361)
(112,362)(113,363)(114,364)(115,365)(116,366)(117,367)(118,368)(119,369)
(120,370)(121,371)(122,372)(123,373)(124,374)(125,375)(126,376)(127,377)
(128,378)(129,379)(130,380)(131,381)(132,382)(133,383)(134,384)(135,385)
(136,386)(137,387)(138,388)(139,389)(140,390)(141,391)(142,392)(143,393)
(144,394)(145,395)(146,396)(147,397)(148,398)(149,399)(150,400)(151,301)
(152,302)(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)
(160,310)(161,311)(162,312)(163,313)(164,314)(165,315)(166,316)(167,317)
(168,318)(169,319)(170,320)(171,321)(172,322)(173,323)(174,324)(175,325)
(176,326)(177,327)(178,328)(179,329)(180,330)(181,331)(182,332)(183,333)
(184,334)(185,335)(186,336)(187,337)(188,338)(189,339)(190,340)(191,341)
(192,342)(193,343)(194,344)(195,345)(196,346)(197,347)(198,348)(199,349)
(200,350);
poly := sub<Sym(400)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope