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