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Polytope of Type {20,10,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,10,4}*1600b
if this polytope has a name.
Group : SmallGroup(1600,8517)
Rank : 4
Schlafli Type : {20,10,4}
Number of vertices, edges, etc : 20, 100, 20, 4
Order of s0s1s2s3 : 20
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 : {20,10,2}*800b, {10,10,4}*800c
   4-fold quotients : {5,10,4}*400, {10,10,2}*400c
   5-fold quotients : {20,2,4}*320
   8-fold quotients : {5,10,2}*200
   10-fold quotients : {20,2,2}*160, {10,2,4}*160
   20-fold quotients : {5,2,4}*80, {10,2,2}*80
   25-fold quotients : {4,2,4}*64
   40-fold quotients : {5,2,2}*40
   50-fold quotients : {2,2,4}*32, {4,2,2}*32
   100-fold quotients : {2,2,2}*16
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)
(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)(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)(301,351)(302,355)(303,354)(304,353)(305,352)(306,371)
(307,375)(308,374)(309,373)(310,372)(311,366)(312,370)(313,369)(314,368)
(315,367)(316,361)(317,365)(318,364)(319,363)(320,362)(321,356)(322,360)
(323,359)(324,358)(325,357)(326,376)(327,380)(328,379)(329,378)(330,377)
(331,396)(332,400)(333,399)(334,398)(335,397)(336,391)(337,395)(338,394)
(339,393)(340,392)(341,386)(342,390)(343,389)(344,388)(345,387)(346,381)
(347,385)(348,384)(349,383)(350,382);;
s1 := (  1,107)(  2,106)(  3,110)(  4,109)(  5,108)(  6,102)(  7,101)(  8,105)
(  9,104)( 10,103)( 11,122)( 12,121)( 13,125)( 14,124)( 15,123)( 16,117)
( 17,116)( 18,120)( 19,119)( 20,118)( 21,112)( 22,111)( 23,115)( 24,114)
( 25,113)( 26,132)( 27,131)( 28,135)( 29,134)( 30,133)( 31,127)( 32,126)
( 33,130)( 34,129)( 35,128)( 36,147)( 37,146)( 38,150)( 39,149)( 40,148)
( 41,142)( 42,141)( 43,145)( 44,144)( 45,143)( 46,137)( 47,136)( 48,140)
( 49,139)( 50,138)( 51,157)( 52,156)( 53,160)( 54,159)( 55,158)( 56,152)
( 57,151)( 58,155)( 59,154)( 60,153)( 61,172)( 62,171)( 63,175)( 64,174)
( 65,173)( 66,167)( 67,166)( 68,170)( 69,169)( 70,168)( 71,162)( 72,161)
( 73,165)( 74,164)( 75,163)( 76,182)( 77,181)( 78,185)( 79,184)( 80,183)
( 81,177)( 82,176)( 83,180)( 84,179)( 85,178)( 86,197)( 87,196)( 88,200)
( 89,199)( 90,198)( 91,192)( 92,191)( 93,195)( 94,194)( 95,193)( 96,187)
( 97,186)( 98,190)( 99,189)(100,188)(201,307)(202,306)(203,310)(204,309)
(205,308)(206,302)(207,301)(208,305)(209,304)(210,303)(211,322)(212,321)
(213,325)(214,324)(215,323)(216,317)(217,316)(218,320)(219,319)(220,318)
(221,312)(222,311)(223,315)(224,314)(225,313)(226,332)(227,331)(228,335)
(229,334)(230,333)(231,327)(232,326)(233,330)(234,329)(235,328)(236,347)
(237,346)(238,350)(239,349)(240,348)(241,342)(242,341)(243,345)(244,344)
(245,343)(246,337)(247,336)(248,340)(249,339)(250,338)(251,357)(252,356)
(253,360)(254,359)(255,358)(256,352)(257,351)(258,355)(259,354)(260,353)
(261,372)(262,371)(263,375)(264,374)(265,373)(266,367)(267,366)(268,370)
(269,369)(270,368)(271,362)(272,361)(273,365)(274,364)(275,363)(276,382)
(277,381)(278,385)(279,384)(280,383)(281,377)(282,376)(283,380)(284,379)
(285,378)(286,397)(287,396)(288,400)(289,399)(290,398)(291,392)(292,391)
(293,395)(294,394)(295,393)(296,387)(297,386)(298,390)(299,389)(300,388);;
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)
(201,226)(202,227)(203,228)(204,229)(205,230)(206,246)(207,247)(208,248)
(209,249)(210,250)(211,241)(212,242)(213,243)(214,244)(215,245)(216,236)
(217,237)(218,238)(219,239)(220,240)(221,231)(222,232)(223,233)(224,234)
(225,235)(251,276)(252,277)(253,278)(254,279)(255,280)(256,296)(257,297)
(258,298)(259,299)(260,300)(261,291)(262,292)(263,293)(264,294)(265,295)
(266,286)(267,287)(268,288)(269,289)(270,290)(271,281)(272,282)(273,283)
(274,284)(275,285)(301,326)(302,327)(303,328)(304,329)(305,330)(306,346)
(307,347)(308,348)(309,349)(310,350)(311,341)(312,342)(313,343)(314,344)
(315,345)(316,336)(317,337)(318,338)(319,339)(320,340)(321,331)(322,332)
(323,333)(324,334)(325,335)(351,376)(352,377)(353,378)(354,379)(355,380)
(356,396)(357,397)(358,398)(359,399)(360,400)(361,391)(362,392)(363,393)
(364,394)(365,395)(366,386)(367,387)(368,388)(369,389)(370,390)(371,381)
(372,382)(373,383)(374,384)(375,385);;
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)( 51,251)( 52,252)( 53,253)( 54,254)( 55,255)( 56,256)
( 57,257)( 58,258)( 59,259)( 60,260)( 61,261)( 62,262)( 63,263)( 64,264)
( 65,265)( 66,266)( 67,267)( 68,268)( 69,269)( 70,270)( 71,271)( 72,272)
( 73,273)( 74,274)( 75,275)( 76,276)( 77,277)( 78,278)( 79,279)( 80,280)
( 81,281)( 82,282)( 83,283)( 84,284)( 85,285)( 86,286)( 87,287)( 88,288)
( 89,289)( 90,290)( 91,291)( 92,292)( 93,293)( 94,294)( 95,295)( 96,296)
( 97,297)( 98,298)( 99,299)(100,300)(101,301)(102,302)(103,303)(104,304)
(105,305)(106,306)(107,307)(108,308)(109,309)(110,310)(111,311)(112,312)
(113,313)(114,314)(115,315)(116,316)(117,317)(118,318)(119,319)(120,320)
(121,321)(122,322)(123,323)(124,324)(125,325)(126,326)(127,327)(128,328)
(129,329)(130,330)(131,331)(132,332)(133,333)(134,334)(135,335)(136,336)
(137,337)(138,338)(139,339)(140,340)(141,341)(142,342)(143,343)(144,344)
(145,345)(146,346)(147,347)(148,348)(149,349)(150,350)(151,351)(152,352)
(153,353)(154,354)(155,355)(156,356)(157,357)(158,358)(159,359)(160,360)
(161,361)(162,362)(163,363)(164,364)(165,365)(166,366)(167,367)(168,368)
(169,369)(170,370)(171,371)(172,372)(173,373)(174,374)(175,375)(176,376)
(177,377)(178,378)(179,379)(180,380)(181,381)(182,382)(183,383)(184,384)
(185,385)(186,386)(187,387)(188,388)(189,389)(190,390)(191,391)(192,392)
(193,393)(194,394)(195,395)(196,396)(197,397)(198,398)(199,399)(200,400);;
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*s3*s2*s3*s2*s3*s2*s3, 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 ];;
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)(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)(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)(301,351)(302,355)(303,354)(304,353)(305,352)
(306,371)(307,375)(308,374)(309,373)(310,372)(311,366)(312,370)(313,369)
(314,368)(315,367)(316,361)(317,365)(318,364)(319,363)(320,362)(321,356)
(322,360)(323,359)(324,358)(325,357)(326,376)(327,380)(328,379)(329,378)
(330,377)(331,396)(332,400)(333,399)(334,398)(335,397)(336,391)(337,395)
(338,394)(339,393)(340,392)(341,386)(342,390)(343,389)(344,388)(345,387)
(346,381)(347,385)(348,384)(349,383)(350,382);
s1 := Sym(400)!(  1,107)(  2,106)(  3,110)(  4,109)(  5,108)(  6,102)(  7,101)
(  8,105)(  9,104)( 10,103)( 11,122)( 12,121)( 13,125)( 14,124)( 15,123)
( 16,117)( 17,116)( 18,120)( 19,119)( 20,118)( 21,112)( 22,111)( 23,115)
( 24,114)( 25,113)( 26,132)( 27,131)( 28,135)( 29,134)( 30,133)( 31,127)
( 32,126)( 33,130)( 34,129)( 35,128)( 36,147)( 37,146)( 38,150)( 39,149)
( 40,148)( 41,142)( 42,141)( 43,145)( 44,144)( 45,143)( 46,137)( 47,136)
( 48,140)( 49,139)( 50,138)( 51,157)( 52,156)( 53,160)( 54,159)( 55,158)
( 56,152)( 57,151)( 58,155)( 59,154)( 60,153)( 61,172)( 62,171)( 63,175)
( 64,174)( 65,173)( 66,167)( 67,166)( 68,170)( 69,169)( 70,168)( 71,162)
( 72,161)( 73,165)( 74,164)( 75,163)( 76,182)( 77,181)( 78,185)( 79,184)
( 80,183)( 81,177)( 82,176)( 83,180)( 84,179)( 85,178)( 86,197)( 87,196)
( 88,200)( 89,199)( 90,198)( 91,192)( 92,191)( 93,195)( 94,194)( 95,193)
( 96,187)( 97,186)( 98,190)( 99,189)(100,188)(201,307)(202,306)(203,310)
(204,309)(205,308)(206,302)(207,301)(208,305)(209,304)(210,303)(211,322)
(212,321)(213,325)(214,324)(215,323)(216,317)(217,316)(218,320)(219,319)
(220,318)(221,312)(222,311)(223,315)(224,314)(225,313)(226,332)(227,331)
(228,335)(229,334)(230,333)(231,327)(232,326)(233,330)(234,329)(235,328)
(236,347)(237,346)(238,350)(239,349)(240,348)(241,342)(242,341)(243,345)
(244,344)(245,343)(246,337)(247,336)(248,340)(249,339)(250,338)(251,357)
(252,356)(253,360)(254,359)(255,358)(256,352)(257,351)(258,355)(259,354)
(260,353)(261,372)(262,371)(263,375)(264,374)(265,373)(266,367)(267,366)
(268,370)(269,369)(270,368)(271,362)(272,361)(273,365)(274,364)(275,363)
(276,382)(277,381)(278,385)(279,384)(280,383)(281,377)(282,376)(283,380)
(284,379)(285,378)(286,397)(287,396)(288,400)(289,399)(290,398)(291,392)
(292,391)(293,395)(294,394)(295,393)(296,387)(297,386)(298,390)(299,389)
(300,388);
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)(201,226)(202,227)(203,228)(204,229)(205,230)(206,246)(207,247)
(208,248)(209,249)(210,250)(211,241)(212,242)(213,243)(214,244)(215,245)
(216,236)(217,237)(218,238)(219,239)(220,240)(221,231)(222,232)(223,233)
(224,234)(225,235)(251,276)(252,277)(253,278)(254,279)(255,280)(256,296)
(257,297)(258,298)(259,299)(260,300)(261,291)(262,292)(263,293)(264,294)
(265,295)(266,286)(267,287)(268,288)(269,289)(270,290)(271,281)(272,282)
(273,283)(274,284)(275,285)(301,326)(302,327)(303,328)(304,329)(305,330)
(306,346)(307,347)(308,348)(309,349)(310,350)(311,341)(312,342)(313,343)
(314,344)(315,345)(316,336)(317,337)(318,338)(319,339)(320,340)(321,331)
(322,332)(323,333)(324,334)(325,335)(351,376)(352,377)(353,378)(354,379)
(355,380)(356,396)(357,397)(358,398)(359,399)(360,400)(361,391)(362,392)
(363,393)(364,394)(365,395)(366,386)(367,387)(368,388)(369,389)(370,390)
(371,381)(372,382)(373,383)(374,384)(375,385);
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)( 51,251)( 52,252)( 53,253)( 54,254)( 55,255)
( 56,256)( 57,257)( 58,258)( 59,259)( 60,260)( 61,261)( 62,262)( 63,263)
( 64,264)( 65,265)( 66,266)( 67,267)( 68,268)( 69,269)( 70,270)( 71,271)
( 72,272)( 73,273)( 74,274)( 75,275)( 76,276)( 77,277)( 78,278)( 79,279)
( 80,280)( 81,281)( 82,282)( 83,283)( 84,284)( 85,285)( 86,286)( 87,287)
( 88,288)( 89,289)( 90,290)( 91,291)( 92,292)( 93,293)( 94,294)( 95,295)
( 96,296)( 97,297)( 98,298)( 99,299)(100,300)(101,301)(102,302)(103,303)
(104,304)(105,305)(106,306)(107,307)(108,308)(109,309)(110,310)(111,311)
(112,312)(113,313)(114,314)(115,315)(116,316)(117,317)(118,318)(119,319)
(120,320)(121,321)(122,322)(123,323)(124,324)(125,325)(126,326)(127,327)
(128,328)(129,329)(130,330)(131,331)(132,332)(133,333)(134,334)(135,335)
(136,336)(137,337)(138,338)(139,339)(140,340)(141,341)(142,342)(143,343)
(144,344)(145,345)(146,346)(147,347)(148,348)(149,349)(150,350)(151,351)
(152,352)(153,353)(154,354)(155,355)(156,356)(157,357)(158,358)(159,359)
(160,360)(161,361)(162,362)(163,363)(164,364)(165,365)(166,366)(167,367)
(168,368)(169,369)(170,370)(171,371)(172,372)(173,373)(174,374)(175,375)
(176,376)(177,377)(178,378)(179,379)(180,380)(181,381)(182,382)(183,383)
(184,384)(185,385)(186,386)(187,387)(188,388)(189,389)(190,390)(191,391)
(192,392)(193,393)(194,394)(195,395)(196,396)(197,397)(198,398)(199,399)
(200,400);
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*s3*s2*s3*s2*s3*s2*s3, 
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 >; 
 
References : None.
to this polytope