Polytope of Type {20,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,4,6}*1440
if this polytope has a name.
Group : SmallGroup(1440,4764)
Rank : 4
Schlafli Type : {20,4,6}
Number of vertices, edges, etc : 20, 60, 18, 9
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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 : {10,4,6}*720
5-fold quotients : {4,4,6}*288
10-fold quotients : {2,4,6}*144
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)
( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)
(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)(118,119)
(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)
(142,145)(143,144)(147,150)(148,149)(152,155)(153,154)(157,160)(158,159)
(162,165)(163,164)(167,170)(168,169)(172,175)(173,174)(177,180)(178,179)
(181,226)(182,230)(183,229)(184,228)(185,227)(186,231)(187,235)(188,234)
(189,233)(190,232)(191,236)(192,240)(193,239)(194,238)(195,237)(196,241)
(197,245)(198,244)(199,243)(200,242)(201,246)(202,250)(203,249)(204,248)
(205,247)(206,251)(207,255)(208,254)(209,253)(210,252)(211,256)(212,260)
(213,259)(214,258)(215,257)(216,261)(217,265)(218,264)(219,263)(220,262)
(221,266)(222,270)(223,269)(224,268)(225,267)(271,316)(272,320)(273,319)
(274,318)(275,317)(276,321)(277,325)(278,324)(279,323)(280,322)(281,326)
(282,330)(283,329)(284,328)(285,327)(286,331)(287,335)(288,334)(289,333)
(290,332)(291,336)(292,340)(293,339)(294,338)(295,337)(296,341)(297,345)
(298,344)(299,343)(300,342)(301,346)(302,350)(303,349)(304,348)(305,347)
(306,351)(307,355)(308,354)(309,353)(310,352)(311,356)(312,360)(313,359)
(314,358)(315,357);;
s1 := ( 1,182)( 2,181)( 3,185)( 4,184)( 5,183)( 6,187)( 7,186)( 8,190)
( 9,189)( 10,188)( 11,192)( 12,191)( 13,195)( 14,194)( 15,193)( 16,222)
( 17,221)( 18,225)( 19,224)( 20,223)( 21,212)( 22,211)( 23,215)( 24,214)
( 25,213)( 26,217)( 27,216)( 28,220)( 29,219)( 30,218)( 31,202)( 32,201)
( 33,205)( 34,204)( 35,203)( 36,207)( 37,206)( 38,210)( 39,209)( 40,208)
( 41,197)( 42,196)( 43,200)( 44,199)( 45,198)( 46,227)( 47,226)( 48,230)
( 49,229)( 50,228)( 51,232)( 52,231)( 53,235)( 54,234)( 55,233)( 56,237)
( 57,236)( 58,240)( 59,239)( 60,238)( 61,267)( 62,266)( 63,270)( 64,269)
( 65,268)( 66,257)( 67,256)( 68,260)( 69,259)( 70,258)( 71,262)( 72,261)
( 73,265)( 74,264)( 75,263)( 76,247)( 77,246)( 78,250)( 79,249)( 80,248)
( 81,252)( 82,251)( 83,255)( 84,254)( 85,253)( 86,242)( 87,241)( 88,245)
( 89,244)( 90,243)( 91,272)( 92,271)( 93,275)( 94,274)( 95,273)( 96,277)
( 97,276)( 98,280)( 99,279)(100,278)(101,282)(102,281)(103,285)(104,284)
(105,283)(106,312)(107,311)(108,315)(109,314)(110,313)(111,302)(112,301)
(113,305)(114,304)(115,303)(116,307)(117,306)(118,310)(119,309)(120,308)
(121,292)(122,291)(123,295)(124,294)(125,293)(126,297)(127,296)(128,300)
(129,299)(130,298)(131,287)(132,286)(133,290)(134,289)(135,288)(136,317)
(137,316)(138,320)(139,319)(140,318)(141,322)(142,321)(143,325)(144,324)
(145,323)(146,327)(147,326)(148,330)(149,329)(150,328)(151,357)(152,356)
(153,360)(154,359)(155,358)(156,347)(157,346)(158,350)(159,349)(160,348)
(161,352)(162,351)(163,355)(164,354)(165,353)(166,337)(167,336)(168,340)
(169,339)(170,338)(171,342)(172,341)(173,345)(174,344)(175,343)(176,332)
(177,331)(178,335)(179,334)(180,333);;
s2 := ( 6, 36)( 7, 37)( 8, 38)( 9, 39)( 10, 40)( 11, 26)( 12, 27)( 13, 28)
( 14, 29)( 15, 30)( 16, 31)( 17, 32)( 18, 33)( 19, 34)( 20, 35)( 51, 81)
( 52, 82)( 53, 83)( 54, 84)( 55, 85)( 56, 71)( 57, 72)( 58, 73)( 59, 74)
( 60, 75)( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 96,126)( 97,127)
( 98,128)( 99,129)(100,130)(101,116)(102,117)(103,118)(104,119)(105,120)
(106,121)(107,122)(108,123)(109,124)(110,125)(141,171)(142,172)(143,173)
(144,174)(145,175)(146,161)(147,162)(148,163)(149,164)(150,165)(151,166)
(152,167)(153,168)(154,169)(155,170)(181,271)(182,272)(183,273)(184,274)
(185,275)(186,306)(187,307)(188,308)(189,309)(190,310)(191,296)(192,297)
(193,298)(194,299)(195,300)(196,301)(197,302)(198,303)(199,304)(200,305)
(201,291)(202,292)(203,293)(204,294)(205,295)(206,281)(207,282)(208,283)
(209,284)(210,285)(211,286)(212,287)(213,288)(214,289)(215,290)(216,276)
(217,277)(218,278)(219,279)(220,280)(221,311)(222,312)(223,313)(224,314)
(225,315)(226,316)(227,317)(228,318)(229,319)(230,320)(231,351)(232,352)
(233,353)(234,354)(235,355)(236,341)(237,342)(238,343)(239,344)(240,345)
(241,346)(242,347)(243,348)(244,349)(245,350)(246,336)(247,337)(248,338)
(249,339)(250,340)(251,326)(252,327)(253,328)(254,329)(255,330)(256,331)
(257,332)(258,333)(259,334)(260,335)(261,321)(262,322)(263,323)(264,324)
(265,325)(266,356)(267,357)(268,358)(269,359)(270,360);;
s3 := ( 1, 96)( 2, 97)( 3, 98)( 4, 99)( 5,100)( 6, 91)( 7, 92)( 8, 93)
( 9, 94)( 10, 95)( 11,101)( 12,102)( 13,103)( 14,104)( 15,105)( 16,126)
( 17,127)( 18,128)( 19,129)( 20,130)( 21,121)( 22,122)( 23,123)( 24,124)
( 25,125)( 26,131)( 27,132)( 28,133)( 29,134)( 30,135)( 31,111)( 32,112)
( 33,113)( 34,114)( 35,115)( 36,106)( 37,107)( 38,108)( 39,109)( 40,110)
( 41,116)( 42,117)( 43,118)( 44,119)( 45,120)( 46,141)( 47,142)( 48,143)
( 49,144)( 50,145)( 51,136)( 52,137)( 53,138)( 54,139)( 55,140)( 56,146)
( 57,147)( 58,148)( 59,149)( 60,150)( 61,171)( 62,172)( 63,173)( 64,174)
( 65,175)( 66,166)( 67,167)( 68,168)( 69,169)( 70,170)( 71,176)( 72,177)
( 73,178)( 74,179)( 75,180)( 76,156)( 77,157)( 78,158)( 79,159)( 80,160)
( 81,151)( 82,152)( 83,153)( 84,154)( 85,155)( 86,161)( 87,162)( 88,163)
( 89,164)( 90,165)(181,276)(182,277)(183,278)(184,279)(185,280)(186,271)
(187,272)(188,273)(189,274)(190,275)(191,281)(192,282)(193,283)(194,284)
(195,285)(196,306)(197,307)(198,308)(199,309)(200,310)(201,301)(202,302)
(203,303)(204,304)(205,305)(206,311)(207,312)(208,313)(209,314)(210,315)
(211,291)(212,292)(213,293)(214,294)(215,295)(216,286)(217,287)(218,288)
(219,289)(220,290)(221,296)(222,297)(223,298)(224,299)(225,300)(226,321)
(227,322)(228,323)(229,324)(230,325)(231,316)(232,317)(233,318)(234,319)
(235,320)(236,326)(237,327)(238,328)(239,329)(240,330)(241,351)(242,352)
(243,353)(244,354)(245,355)(246,346)(247,347)(248,348)(249,349)(250,350)
(251,356)(252,357)(253,358)(254,359)(255,360)(256,336)(257,337)(258,338)
(259,339)(260,340)(261,331)(262,332)(263,333)(264,334)(265,335)(266,341)
(267,342)(268,343)(269,344)(270,345);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(360)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)
( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)
( 98, 99)(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)
(118,119)(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)
(138,139)(142,145)(143,144)(147,150)(148,149)(152,155)(153,154)(157,160)
(158,159)(162,165)(163,164)(167,170)(168,169)(172,175)(173,174)(177,180)
(178,179)(181,226)(182,230)(183,229)(184,228)(185,227)(186,231)(187,235)
(188,234)(189,233)(190,232)(191,236)(192,240)(193,239)(194,238)(195,237)
(196,241)(197,245)(198,244)(199,243)(200,242)(201,246)(202,250)(203,249)
(204,248)(205,247)(206,251)(207,255)(208,254)(209,253)(210,252)(211,256)
(212,260)(213,259)(214,258)(215,257)(216,261)(217,265)(218,264)(219,263)
(220,262)(221,266)(222,270)(223,269)(224,268)(225,267)(271,316)(272,320)
(273,319)(274,318)(275,317)(276,321)(277,325)(278,324)(279,323)(280,322)
(281,326)(282,330)(283,329)(284,328)(285,327)(286,331)(287,335)(288,334)
(289,333)(290,332)(291,336)(292,340)(293,339)(294,338)(295,337)(296,341)
(297,345)(298,344)(299,343)(300,342)(301,346)(302,350)(303,349)(304,348)
(305,347)(306,351)(307,355)(308,354)(309,353)(310,352)(311,356)(312,360)
(313,359)(314,358)(315,357);
s1 := Sym(360)!( 1,182)( 2,181)( 3,185)( 4,184)( 5,183)( 6,187)( 7,186)
( 8,190)( 9,189)( 10,188)( 11,192)( 12,191)( 13,195)( 14,194)( 15,193)
( 16,222)( 17,221)( 18,225)( 19,224)( 20,223)( 21,212)( 22,211)( 23,215)
( 24,214)( 25,213)( 26,217)( 27,216)( 28,220)( 29,219)( 30,218)( 31,202)
( 32,201)( 33,205)( 34,204)( 35,203)( 36,207)( 37,206)( 38,210)( 39,209)
( 40,208)( 41,197)( 42,196)( 43,200)( 44,199)( 45,198)( 46,227)( 47,226)
( 48,230)( 49,229)( 50,228)( 51,232)( 52,231)( 53,235)( 54,234)( 55,233)
( 56,237)( 57,236)( 58,240)( 59,239)( 60,238)( 61,267)( 62,266)( 63,270)
( 64,269)( 65,268)( 66,257)( 67,256)( 68,260)( 69,259)( 70,258)( 71,262)
( 72,261)( 73,265)( 74,264)( 75,263)( 76,247)( 77,246)( 78,250)( 79,249)
( 80,248)( 81,252)( 82,251)( 83,255)( 84,254)( 85,253)( 86,242)( 87,241)
( 88,245)( 89,244)( 90,243)( 91,272)( 92,271)( 93,275)( 94,274)( 95,273)
( 96,277)( 97,276)( 98,280)( 99,279)(100,278)(101,282)(102,281)(103,285)
(104,284)(105,283)(106,312)(107,311)(108,315)(109,314)(110,313)(111,302)
(112,301)(113,305)(114,304)(115,303)(116,307)(117,306)(118,310)(119,309)
(120,308)(121,292)(122,291)(123,295)(124,294)(125,293)(126,297)(127,296)
(128,300)(129,299)(130,298)(131,287)(132,286)(133,290)(134,289)(135,288)
(136,317)(137,316)(138,320)(139,319)(140,318)(141,322)(142,321)(143,325)
(144,324)(145,323)(146,327)(147,326)(148,330)(149,329)(150,328)(151,357)
(152,356)(153,360)(154,359)(155,358)(156,347)(157,346)(158,350)(159,349)
(160,348)(161,352)(162,351)(163,355)(164,354)(165,353)(166,337)(167,336)
(168,340)(169,339)(170,338)(171,342)(172,341)(173,345)(174,344)(175,343)
(176,332)(177,331)(178,335)(179,334)(180,333);
s2 := Sym(360)!( 6, 36)( 7, 37)( 8, 38)( 9, 39)( 10, 40)( 11, 26)( 12, 27)
( 13, 28)( 14, 29)( 15, 30)( 16, 31)( 17, 32)( 18, 33)( 19, 34)( 20, 35)
( 51, 81)( 52, 82)( 53, 83)( 54, 84)( 55, 85)( 56, 71)( 57, 72)( 58, 73)
( 59, 74)( 60, 75)( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 96,126)
( 97,127)( 98,128)( 99,129)(100,130)(101,116)(102,117)(103,118)(104,119)
(105,120)(106,121)(107,122)(108,123)(109,124)(110,125)(141,171)(142,172)
(143,173)(144,174)(145,175)(146,161)(147,162)(148,163)(149,164)(150,165)
(151,166)(152,167)(153,168)(154,169)(155,170)(181,271)(182,272)(183,273)
(184,274)(185,275)(186,306)(187,307)(188,308)(189,309)(190,310)(191,296)
(192,297)(193,298)(194,299)(195,300)(196,301)(197,302)(198,303)(199,304)
(200,305)(201,291)(202,292)(203,293)(204,294)(205,295)(206,281)(207,282)
(208,283)(209,284)(210,285)(211,286)(212,287)(213,288)(214,289)(215,290)
(216,276)(217,277)(218,278)(219,279)(220,280)(221,311)(222,312)(223,313)
(224,314)(225,315)(226,316)(227,317)(228,318)(229,319)(230,320)(231,351)
(232,352)(233,353)(234,354)(235,355)(236,341)(237,342)(238,343)(239,344)
(240,345)(241,346)(242,347)(243,348)(244,349)(245,350)(246,336)(247,337)
(248,338)(249,339)(250,340)(251,326)(252,327)(253,328)(254,329)(255,330)
(256,331)(257,332)(258,333)(259,334)(260,335)(261,321)(262,322)(263,323)
(264,324)(265,325)(266,356)(267,357)(268,358)(269,359)(270,360);
s3 := Sym(360)!( 1, 96)( 2, 97)( 3, 98)( 4, 99)( 5,100)( 6, 91)( 7, 92)
( 8, 93)( 9, 94)( 10, 95)( 11,101)( 12,102)( 13,103)( 14,104)( 15,105)
( 16,126)( 17,127)( 18,128)( 19,129)( 20,130)( 21,121)( 22,122)( 23,123)
( 24,124)( 25,125)( 26,131)( 27,132)( 28,133)( 29,134)( 30,135)( 31,111)
( 32,112)( 33,113)( 34,114)( 35,115)( 36,106)( 37,107)( 38,108)( 39,109)
( 40,110)( 41,116)( 42,117)( 43,118)( 44,119)( 45,120)( 46,141)( 47,142)
( 48,143)( 49,144)( 50,145)( 51,136)( 52,137)( 53,138)( 54,139)( 55,140)
( 56,146)( 57,147)( 58,148)( 59,149)( 60,150)( 61,171)( 62,172)( 63,173)
( 64,174)( 65,175)( 66,166)( 67,167)( 68,168)( 69,169)( 70,170)( 71,176)
( 72,177)( 73,178)( 74,179)( 75,180)( 76,156)( 77,157)( 78,158)( 79,159)
( 80,160)( 81,151)( 82,152)( 83,153)( 84,154)( 85,155)( 86,161)( 87,162)
( 88,163)( 89,164)( 90,165)(181,276)(182,277)(183,278)(184,279)(185,280)
(186,271)(187,272)(188,273)(189,274)(190,275)(191,281)(192,282)(193,283)
(194,284)(195,285)(196,306)(197,307)(198,308)(199,309)(200,310)(201,301)
(202,302)(203,303)(204,304)(205,305)(206,311)(207,312)(208,313)(209,314)
(210,315)(211,291)(212,292)(213,293)(214,294)(215,295)(216,286)(217,287)
(218,288)(219,289)(220,290)(221,296)(222,297)(223,298)(224,299)(225,300)
(226,321)(227,322)(228,323)(229,324)(230,325)(231,316)(232,317)(233,318)
(234,319)(235,320)(236,326)(237,327)(238,328)(239,329)(240,330)(241,351)
(242,352)(243,353)(244,354)(245,355)(246,346)(247,347)(248,348)(249,349)
(250,350)(251,356)(252,357)(253,358)(254,359)(255,360)(256,336)(257,337)
(258,338)(259,339)(260,340)(261,331)(262,332)(263,333)(264,334)(265,335)
(266,341)(267,342)(268,343)(269,344)(270,345);
poly := sub<Sym(360)|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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*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 >;
References : None.
to this polytope