Polytope of Type {2,4,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,20}*1280c
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, 91)( 4, 92)( 5, 93)( 6, 94)( 7, 95)( 8, 96)( 9, 97)( 10, 98)
( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)
( 19,107)( 20,108)( 21,109)( 22,110)( 23,111)( 24,112)( 25,113)( 26,114)
( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)( 34,106)
( 35,123)( 36,124)( 37,125)( 38,126)( 39,127)( 40,128)( 41,129)( 42,130)
( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)( 49,121)( 50,122)
( 51,139)( 52,140)( 53,141)( 54,142)( 55,143)( 56,144)( 57,145)( 58,146)
( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)( 65,137)( 66,138)
( 67,155)( 68,156)( 69,157)( 70,158)( 71,159)( 72,160)( 73,161)( 74,162)
( 75,147)( 76,148)( 77,149)( 78,150)( 79,151)( 80,152)( 81,153)( 82,154)
(163,251)(164,252)(165,253)(166,254)(167,255)(168,256)(169,257)(170,258)
(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)(177,249)(178,250)
(179,267)(180,268)(181,269)(182,270)(183,271)(184,272)(185,273)(186,274)
(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)(193,265)(194,266)
(195,283)(196,284)(197,285)(198,286)(199,287)(200,288)(201,289)(202,290)
(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)(209,281)(210,282)
(211,299)(212,300)(213,301)(214,302)(215,303)(216,304)(217,305)(218,306)
(219,291)(220,292)(221,293)(222,294)(223,295)(224,296)(225,297)(226,298)
(227,315)(228,316)(229,317)(230,318)(231,319)(232,320)(233,321)(234,322)
(235,307)(236,308)(237,309)(238,310)(239,311)(240,312)(241,313)(242,314);;
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,
s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2,
s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(322)!(1,2);
s1 := Sym(322)!( 3, 91)( 4, 92)( 5, 93)( 6, 94)( 7, 95)( 8, 96)( 9, 97)
( 10, 98)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)
( 18, 90)( 19,107)( 20,108)( 21,109)( 22,110)( 23,111)( 24,112)( 25,113)
( 26,114)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)
( 34,106)( 35,123)( 36,124)( 37,125)( 38,126)( 39,127)( 40,128)( 41,129)
( 42,130)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)( 49,121)
( 50,122)( 51,139)( 52,140)( 53,141)( 54,142)( 55,143)( 56,144)( 57,145)
( 58,146)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)( 65,137)
( 66,138)( 67,155)( 68,156)( 69,157)( 70,158)( 71,159)( 72,160)( 73,161)
( 74,162)( 75,147)( 76,148)( 77,149)( 78,150)( 79,151)( 80,152)( 81,153)
( 82,154)(163,251)(164,252)(165,253)(166,254)(167,255)(168,256)(169,257)
(170,258)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)(177,249)
(178,250)(179,267)(180,268)(181,269)(182,270)(183,271)(184,272)(185,273)
(186,274)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)(193,265)
(194,266)(195,283)(196,284)(197,285)(198,286)(199,287)(200,288)(201,289)
(202,290)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)(209,281)
(210,282)(211,299)(212,300)(213,301)(214,302)(215,303)(216,304)(217,305)
(218,306)(219,291)(220,292)(221,293)(222,294)(223,295)(224,296)(225,297)
(226,298)(227,315)(228,316)(229,317)(230,318)(231,319)(232,320)(233,321)
(234,322)(235,307)(236,308)(237,309)(238,310)(239,311)(240,312)(241,313)
(242,314);
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,
s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2,
s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;
to this polytope