Polytope of Type {2,4,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,20}*1280b
if this polytope has a name.
Group : SmallGroup(1280,1116447)
Rank : 4
Schlafli Type : {2,4,20}
Number of vertices, edges, etc : 2, 16, 160, 80
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,4,10}*640a
4-fold quotients : {2,4,5}*320
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)( 10, 18)
( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)( 26, 34)
( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)( 42, 50)
( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)( 58, 66)
( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)( 74, 82)
( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)
( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)
(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(121,129)(122,130)
(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146)
(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(153,161)(154,162)
(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(169,177)(170,178)
(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(185,193)(186,194)
(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)(201,209)(202,210)
(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)(217,225)(218,226)
(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)(233,241)(234,242)
(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)(249,257)(250,258)
(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)(265,273)(266,274)
(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)(281,289)(282,290)
(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)(297,305)(298,306)
(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)(313,321)(314,322);;
s2 := ( 4, 11)( 5, 18)( 6, 10)( 8, 15)( 9, 14)( 13, 17)( 19, 67)( 20, 75)
( 21, 82)( 22, 74)( 23, 71)( 24, 79)( 25, 78)( 26, 70)( 27, 68)( 28, 76)
( 29, 81)( 30, 73)( 31, 72)( 32, 80)( 33, 77)( 34, 69)( 35, 51)( 36, 59)
( 37, 66)( 38, 58)( 39, 55)( 40, 63)( 41, 62)( 42, 54)( 43, 52)( 44, 60)
( 45, 65)( 46, 57)( 47, 56)( 48, 64)( 49, 61)( 50, 53)( 84, 91)( 85, 98)
( 86, 90)( 88, 95)( 89, 94)( 93, 97)( 99,147)(100,155)(101,162)(102,154)
(103,151)(104,159)(105,158)(106,150)(107,148)(108,156)(109,161)(110,153)
(111,152)(112,160)(113,157)(114,149)(115,131)(116,139)(117,146)(118,138)
(119,135)(120,143)(121,142)(122,134)(123,132)(124,140)(125,145)(126,137)
(127,136)(128,144)(129,141)(130,133)(163,243)(164,251)(165,258)(166,250)
(167,247)(168,255)(169,254)(170,246)(171,244)(172,252)(173,257)(174,249)
(175,248)(176,256)(177,253)(178,245)(179,307)(180,315)(181,322)(182,314)
(183,311)(184,319)(185,318)(186,310)(187,308)(188,316)(189,321)(190,313)
(191,312)(192,320)(193,317)(194,309)(195,291)(196,299)(197,306)(198,298)
(199,295)(200,303)(201,302)(202,294)(203,292)(204,300)(205,305)(206,297)
(207,296)(208,304)(209,301)(210,293)(211,275)(212,283)(213,290)(214,282)
(215,279)(216,287)(217,286)(218,278)(219,276)(220,284)(221,289)(222,281)
(223,280)(224,288)(225,285)(226,277)(227,259)(228,267)(229,274)(230,266)
(231,263)(232,271)(233,270)(234,262)(235,260)(236,268)(237,273)(238,265)
(239,264)(240,272)(241,269)(242,261);;
s3 := ( 3,179)( 4,189)( 5,188)( 6,182)( 7,191)( 8,185)( 9,184)( 10,194)
( 11,187)( 12,181)( 13,180)( 14,190)( 15,183)( 16,193)( 17,192)( 18,186)
( 19,163)( 20,173)( 21,172)( 22,166)( 23,175)( 24,169)( 25,168)( 26,178)
( 27,171)( 28,165)( 29,164)( 30,174)( 31,167)( 32,177)( 33,176)( 34,170)
( 35,227)( 36,237)( 37,236)( 38,230)( 39,239)( 40,233)( 41,232)( 42,242)
( 43,235)( 44,229)( 45,228)( 46,238)( 47,231)( 48,241)( 49,240)( 50,234)
( 51,211)( 52,221)( 53,220)( 54,214)( 55,223)( 56,217)( 57,216)( 58,226)
( 59,219)( 60,213)( 61,212)( 62,222)( 63,215)( 64,225)( 65,224)( 66,218)
( 67,195)( 68,205)( 69,204)( 70,198)( 71,207)( 72,201)( 73,200)( 74,210)
( 75,203)( 76,197)( 77,196)( 78,206)( 79,199)( 80,209)( 81,208)( 82,202)
( 83,259)( 84,269)( 85,268)( 86,262)( 87,271)( 88,265)( 89,264)( 90,274)
( 91,267)( 92,261)( 93,260)( 94,270)( 95,263)( 96,273)( 97,272)( 98,266)
( 99,243)(100,253)(101,252)(102,246)(103,255)(104,249)(105,248)(106,258)
(107,251)(108,245)(109,244)(110,254)(111,247)(112,257)(113,256)(114,250)
(115,307)(116,317)(117,316)(118,310)(119,319)(120,313)(121,312)(122,322)
(123,315)(124,309)(125,308)(126,318)(127,311)(128,321)(129,320)(130,314)
(131,291)(132,301)(133,300)(134,294)(135,303)(136,297)(137,296)(138,306)
(139,299)(140,293)(141,292)(142,302)(143,295)(144,305)(145,304)(146,298)
(147,275)(148,285)(149,284)(150,278)(151,287)(152,281)(153,280)(154,290)
(155,283)(156,277)(157,276)(158,286)(159,279)(160,289)(161,288)(162,282);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(322)!(1,2);
s1 := Sym(322)!( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)
( 10, 18)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)
( 26, 34)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)
( 42, 50)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)
( 58, 66)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)
( 74, 82)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)
( 90, 98)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)
(106,114)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(121,129)
(122,130)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)
(138,146)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(153,161)
(154,162)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(169,177)
(170,178)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(185,193)
(186,194)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)(201,209)
(202,210)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)(217,225)
(218,226)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)(233,241)
(234,242)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)(249,257)
(250,258)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)(265,273)
(266,274)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)(281,289)
(282,290)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)(297,305)
(298,306)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)(313,321)
(314,322);
s2 := Sym(322)!( 4, 11)( 5, 18)( 6, 10)( 8, 15)( 9, 14)( 13, 17)( 19, 67)
( 20, 75)( 21, 82)( 22, 74)( 23, 71)( 24, 79)( 25, 78)( 26, 70)( 27, 68)
( 28, 76)( 29, 81)( 30, 73)( 31, 72)( 32, 80)( 33, 77)( 34, 69)( 35, 51)
( 36, 59)( 37, 66)( 38, 58)( 39, 55)( 40, 63)( 41, 62)( 42, 54)( 43, 52)
( 44, 60)( 45, 65)( 46, 57)( 47, 56)( 48, 64)( 49, 61)( 50, 53)( 84, 91)
( 85, 98)( 86, 90)( 88, 95)( 89, 94)( 93, 97)( 99,147)(100,155)(101,162)
(102,154)(103,151)(104,159)(105,158)(106,150)(107,148)(108,156)(109,161)
(110,153)(111,152)(112,160)(113,157)(114,149)(115,131)(116,139)(117,146)
(118,138)(119,135)(120,143)(121,142)(122,134)(123,132)(124,140)(125,145)
(126,137)(127,136)(128,144)(129,141)(130,133)(163,243)(164,251)(165,258)
(166,250)(167,247)(168,255)(169,254)(170,246)(171,244)(172,252)(173,257)
(174,249)(175,248)(176,256)(177,253)(178,245)(179,307)(180,315)(181,322)
(182,314)(183,311)(184,319)(185,318)(186,310)(187,308)(188,316)(189,321)
(190,313)(191,312)(192,320)(193,317)(194,309)(195,291)(196,299)(197,306)
(198,298)(199,295)(200,303)(201,302)(202,294)(203,292)(204,300)(205,305)
(206,297)(207,296)(208,304)(209,301)(210,293)(211,275)(212,283)(213,290)
(214,282)(215,279)(216,287)(217,286)(218,278)(219,276)(220,284)(221,289)
(222,281)(223,280)(224,288)(225,285)(226,277)(227,259)(228,267)(229,274)
(230,266)(231,263)(232,271)(233,270)(234,262)(235,260)(236,268)(237,273)
(238,265)(239,264)(240,272)(241,269)(242,261);
s3 := Sym(322)!( 3,179)( 4,189)( 5,188)( 6,182)( 7,191)( 8,185)( 9,184)
( 10,194)( 11,187)( 12,181)( 13,180)( 14,190)( 15,183)( 16,193)( 17,192)
( 18,186)( 19,163)( 20,173)( 21,172)( 22,166)( 23,175)( 24,169)( 25,168)
( 26,178)( 27,171)( 28,165)( 29,164)( 30,174)( 31,167)( 32,177)( 33,176)
( 34,170)( 35,227)( 36,237)( 37,236)( 38,230)( 39,239)( 40,233)( 41,232)
( 42,242)( 43,235)( 44,229)( 45,228)( 46,238)( 47,231)( 48,241)( 49,240)
( 50,234)( 51,211)( 52,221)( 53,220)( 54,214)( 55,223)( 56,217)( 57,216)
( 58,226)( 59,219)( 60,213)( 61,212)( 62,222)( 63,215)( 64,225)( 65,224)
( 66,218)( 67,195)( 68,205)( 69,204)( 70,198)( 71,207)( 72,201)( 73,200)
( 74,210)( 75,203)( 76,197)( 77,196)( 78,206)( 79,199)( 80,209)( 81,208)
( 82,202)( 83,259)( 84,269)( 85,268)( 86,262)( 87,271)( 88,265)( 89,264)
( 90,274)( 91,267)( 92,261)( 93,260)( 94,270)( 95,263)( 96,273)( 97,272)
( 98,266)( 99,243)(100,253)(101,252)(102,246)(103,255)(104,249)(105,248)
(106,258)(107,251)(108,245)(109,244)(110,254)(111,247)(112,257)(113,256)
(114,250)(115,307)(116,317)(117,316)(118,310)(119,319)(120,313)(121,312)
(122,322)(123,315)(124,309)(125,308)(126,318)(127,311)(128,321)(129,320)
(130,314)(131,291)(132,301)(133,300)(134,294)(135,303)(136,297)(137,296)
(138,306)(139,299)(140,293)(141,292)(142,302)(143,295)(144,305)(145,304)
(146,298)(147,275)(148,285)(149,284)(150,278)(151,287)(152,281)(153,280)
(154,290)(155,283)(156,277)(157,276)(158,286)(159,279)(160,289)(161,288)
(162,282);
poly := sub<Sym(322)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope