Polytope of Type {4,20,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,20,10}*1600c
if this polytope has a name.
Group : SmallGroup(1600,8970)
Rank : 4
Schlafli Type : {4,20,10}
Number of vertices, edges, etc : 4, 40, 100, 10
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 : {4,10,10}*800c, {2,20,10}*800c
4-fold quotients : {4,10,5}*400, {2,10,10}*400b
5-fold quotients : {4,4,10}*320
8-fold quotients : {2,10,5}*200
10-fold quotients : {2,4,10}*160, {4,2,10}*160
20-fold quotients : {4,2,5}*80, {2,2,10}*80
25-fold quotients : {4,4,2}*64
40-fold quotients : {2,2,5}*40
50-fold quotients : {2,4,2}*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 := ( 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);;
s1 := ( 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)
(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)(201,226)(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)(301,376)(302,377)(303,378)(304,379)
(305,380)(306,396)(307,397)(308,398)(309,399)(310,400)(311,391)(312,392)
(313,393)(314,394)(315,395)(316,386)(317,387)(318,388)(319,389)(320,390)
(321,381)(322,382)(323,383)(324,384)(325,385)(326,351)(327,352)(328,353)
(329,354)(330,355)(331,371)(332,372)(333,373)(334,374)(335,375)(336,366)
(337,367)(338,368)(339,369)(340,370)(341,361)(342,362)(343,363)(344,364)
(345,365)(346,356)(347,357)(348,358)(349,359)(350,360);;
s2 := ( 1,106)( 2,110)( 3,109)( 4,108)( 5,107)( 6,101)( 7,105)( 8,104)
( 9,103)( 10,102)( 11,121)( 12,125)( 13,124)( 14,123)( 15,122)( 16,116)
( 17,120)( 18,119)( 19,118)( 20,117)( 21,111)( 22,115)( 23,114)( 24,113)
( 25,112)( 26,131)( 27,135)( 28,134)( 29,133)( 30,132)( 31,126)( 32,130)
( 33,129)( 34,128)( 35,127)( 36,146)( 37,150)( 38,149)( 39,148)( 40,147)
( 41,141)( 42,145)( 43,144)( 44,143)( 45,142)( 46,136)( 47,140)( 48,139)
( 49,138)( 50,137)( 51,156)( 52,160)( 53,159)( 54,158)( 55,157)( 56,151)
( 57,155)( 58,154)( 59,153)( 60,152)( 61,171)( 62,175)( 63,174)( 64,173)
( 65,172)( 66,166)( 67,170)( 68,169)( 69,168)( 70,167)( 71,161)( 72,165)
( 73,164)( 74,163)( 75,162)( 76,181)( 77,185)( 78,184)( 79,183)( 80,182)
( 81,176)( 82,180)( 83,179)( 84,178)( 85,177)( 86,196)( 87,200)( 88,199)
( 89,198)( 90,197)( 91,191)( 92,195)( 93,194)( 94,193)( 95,192)( 96,186)
( 97,190)( 98,189)( 99,188)(100,187)(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)(251,356)(252,360)
(253,359)(254,358)(255,357)(256,351)(257,355)(258,354)(259,353)(260,352)
(261,371)(262,375)(263,374)(264,373)(265,372)(266,366)(267,370)(268,369)
(269,368)(270,367)(271,361)(272,365)(273,364)(274,363)(275,362)(276,381)
(277,385)(278,384)(279,383)(280,382)(281,376)(282,380)(283,379)(284,378)
(285,377)(286,396)(287,400)(288,399)(289,398)(290,397)(291,391)(292,395)
(293,394)(294,393)(295,392)(296,386)(297,390)(298,389)(299,388)(300,387);;
s3 := ( 1, 2)( 3, 5)( 6, 22)( 7, 21)( 8, 25)( 9, 24)( 10, 23)( 11, 17)
( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 27)( 28, 30)( 31, 47)( 32, 46)
( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)( 40, 43)
( 51, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)( 61, 67)
( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76, 77)( 78, 80)( 81, 97)( 82, 96)
( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)( 90, 93)
(101,102)(103,105)(106,122)(107,121)(108,125)(109,124)(110,123)(111,117)
(112,116)(113,120)(114,119)(115,118)(126,127)(128,130)(131,147)(132,146)
(133,150)(134,149)(135,148)(136,142)(137,141)(138,145)(139,144)(140,143)
(151,152)(153,155)(156,172)(157,171)(158,175)(159,174)(160,173)(161,167)
(162,166)(163,170)(164,169)(165,168)(176,177)(178,180)(181,197)(182,196)
(183,200)(184,199)(185,198)(186,192)(187,191)(188,195)(189,194)(190,193)
(201,202)(203,205)(206,222)(207,221)(208,225)(209,224)(210,223)(211,217)
(212,216)(213,220)(214,219)(215,218)(226,227)(228,230)(231,247)(232,246)
(233,250)(234,249)(235,248)(236,242)(237,241)(238,245)(239,244)(240,243)
(251,252)(253,255)(256,272)(257,271)(258,275)(259,274)(260,273)(261,267)
(262,266)(263,270)(264,269)(265,268)(276,277)(278,280)(281,297)(282,296)
(283,300)(284,299)(285,298)(286,292)(287,291)(288,295)(289,294)(290,293)
(301,302)(303,305)(306,322)(307,321)(308,325)(309,324)(310,323)(311,317)
(312,316)(313,320)(314,319)(315,318)(326,327)(328,330)(331,347)(332,346)
(333,350)(334,349)(335,348)(336,342)(337,341)(338,345)(339,344)(340,343)
(351,352)(353,355)(356,372)(357,371)(358,375)(359,374)(360,373)(361,367)
(362,366)(363,370)(364,369)(365,368)(376,377)(378,380)(381,397)(382,396)
(383,400)(384,399)(385,398)(386,392)(387,391)(388,395)(389,394)(390,393);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
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)!( 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);
s1 := 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)(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)(201,226)(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)(301,376)(302,377)(303,378)
(304,379)(305,380)(306,396)(307,397)(308,398)(309,399)(310,400)(311,391)
(312,392)(313,393)(314,394)(315,395)(316,386)(317,387)(318,388)(319,389)
(320,390)(321,381)(322,382)(323,383)(324,384)(325,385)(326,351)(327,352)
(328,353)(329,354)(330,355)(331,371)(332,372)(333,373)(334,374)(335,375)
(336,366)(337,367)(338,368)(339,369)(340,370)(341,361)(342,362)(343,363)
(344,364)(345,365)(346,356)(347,357)(348,358)(349,359)(350,360);
s2 := Sym(400)!( 1,106)( 2,110)( 3,109)( 4,108)( 5,107)( 6,101)( 7,105)
( 8,104)( 9,103)( 10,102)( 11,121)( 12,125)( 13,124)( 14,123)( 15,122)
( 16,116)( 17,120)( 18,119)( 19,118)( 20,117)( 21,111)( 22,115)( 23,114)
( 24,113)( 25,112)( 26,131)( 27,135)( 28,134)( 29,133)( 30,132)( 31,126)
( 32,130)( 33,129)( 34,128)( 35,127)( 36,146)( 37,150)( 38,149)( 39,148)
( 40,147)( 41,141)( 42,145)( 43,144)( 44,143)( 45,142)( 46,136)( 47,140)
( 48,139)( 49,138)( 50,137)( 51,156)( 52,160)( 53,159)( 54,158)( 55,157)
( 56,151)( 57,155)( 58,154)( 59,153)( 60,152)( 61,171)( 62,175)( 63,174)
( 64,173)( 65,172)( 66,166)( 67,170)( 68,169)( 69,168)( 70,167)( 71,161)
( 72,165)( 73,164)( 74,163)( 75,162)( 76,181)( 77,185)( 78,184)( 79,183)
( 80,182)( 81,176)( 82,180)( 83,179)( 84,178)( 85,177)( 86,196)( 87,200)
( 88,199)( 89,198)( 90,197)( 91,191)( 92,195)( 93,194)( 94,193)( 95,192)
( 96,186)( 97,190)( 98,189)( 99,188)(100,187)(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)(251,356)
(252,360)(253,359)(254,358)(255,357)(256,351)(257,355)(258,354)(259,353)
(260,352)(261,371)(262,375)(263,374)(264,373)(265,372)(266,366)(267,370)
(268,369)(269,368)(270,367)(271,361)(272,365)(273,364)(274,363)(275,362)
(276,381)(277,385)(278,384)(279,383)(280,382)(281,376)(282,380)(283,379)
(284,378)(285,377)(286,396)(287,400)(288,399)(289,398)(290,397)(291,391)
(292,395)(293,394)(294,393)(295,392)(296,386)(297,390)(298,389)(299,388)
(300,387);
s3 := Sym(400)!( 1, 2)( 3, 5)( 6, 22)( 7, 21)( 8, 25)( 9, 24)( 10, 23)
( 11, 17)( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 27)( 28, 30)( 31, 47)
( 32, 46)( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)
( 40, 43)( 51, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)
( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76, 77)( 78, 80)( 81, 97)
( 82, 96)( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)
( 90, 93)(101,102)(103,105)(106,122)(107,121)(108,125)(109,124)(110,123)
(111,117)(112,116)(113,120)(114,119)(115,118)(126,127)(128,130)(131,147)
(132,146)(133,150)(134,149)(135,148)(136,142)(137,141)(138,145)(139,144)
(140,143)(151,152)(153,155)(156,172)(157,171)(158,175)(159,174)(160,173)
(161,167)(162,166)(163,170)(164,169)(165,168)(176,177)(178,180)(181,197)
(182,196)(183,200)(184,199)(185,198)(186,192)(187,191)(188,195)(189,194)
(190,193)(201,202)(203,205)(206,222)(207,221)(208,225)(209,224)(210,223)
(211,217)(212,216)(213,220)(214,219)(215,218)(226,227)(228,230)(231,247)
(232,246)(233,250)(234,249)(235,248)(236,242)(237,241)(238,245)(239,244)
(240,243)(251,252)(253,255)(256,272)(257,271)(258,275)(259,274)(260,273)
(261,267)(262,266)(263,270)(264,269)(265,268)(276,277)(278,280)(281,297)
(282,296)(283,300)(284,299)(285,298)(286,292)(287,291)(288,295)(289,294)
(290,293)(301,302)(303,305)(306,322)(307,321)(308,325)(309,324)(310,323)
(311,317)(312,316)(313,320)(314,319)(315,318)(326,327)(328,330)(331,347)
(332,346)(333,350)(334,349)(335,348)(336,342)(337,341)(338,345)(339,344)
(340,343)(351,352)(353,355)(356,372)(357,371)(358,375)(359,374)(360,373)
(361,367)(362,366)(363,370)(364,369)(365,368)(376,377)(378,380)(381,397)
(382,396)(383,400)(384,399)(385,398)(386,392)(387,391)(388,395)(389,394)
(390,393);
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,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 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