Polytope of Type {2,20,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,4}*1280e
if this polytope has a name.
Group : SmallGroup(1280,1116454)
Rank : 4
Schlafli Type : {2,20,4}
Number of vertices, edges, etc : 2, 80, 160, 16
Order of s0s1s2s3 : 10
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 : {2,10,4}*640b
4-fold quotients : {2,5,4}*320
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 30)( 6, 29)( 7, 17)( 8, 18)( 9, 23)( 10, 24)( 11, 20)( 12, 19)
( 13, 14)( 15, 34)( 16, 33)( 25, 31)( 26, 32)( 27, 28)( 35,131)( 36,132)
( 37,158)( 38,157)( 39,145)( 40,146)( 41,151)( 42,152)( 43,148)( 44,147)
( 45,142)( 46,141)( 47,162)( 48,161)( 49,135)( 50,136)( 51,140)( 52,139)
( 53,149)( 54,150)( 55,137)( 56,138)( 57,159)( 58,160)( 59,156)( 60,155)
( 61,134)( 62,133)( 63,153)( 64,154)( 65,144)( 66,143)( 67, 99)( 68,100)
( 69,126)( 70,125)( 71,113)( 72,114)( 73,119)( 74,120)( 75,116)( 76,115)
( 77,110)( 78,109)( 79,130)( 80,129)( 81,103)( 82,104)( 83,108)( 84,107)
( 85,117)( 86,118)( 87,105)( 88,106)( 89,127)( 90,128)( 91,124)( 92,123)
( 93,102)( 94,101)( 95,121)( 96,122)( 97,112)( 98,111)(163,164)(165,189)
(166,190)(167,178)(168,177)(169,184)(170,183)(171,179)(172,180)(175,193)
(176,194)(181,182)(185,192)(186,191)(195,292)(196,291)(197,317)(198,318)
(199,306)(200,305)(201,312)(202,311)(203,307)(204,308)(205,301)(206,302)
(207,321)(208,322)(209,296)(210,295)(211,299)(212,300)(213,310)(214,309)
(215,298)(216,297)(217,320)(218,319)(219,315)(220,316)(221,293)(222,294)
(223,314)(224,313)(225,303)(226,304)(227,260)(228,259)(229,285)(230,286)
(231,274)(232,273)(233,280)(234,279)(235,275)(236,276)(237,269)(238,270)
(239,289)(240,290)(241,264)(242,263)(243,267)(244,268)(245,278)(246,277)
(247,266)(248,265)(249,288)(250,287)(251,283)(252,284)(253,261)(254,262)
(255,282)(256,281)(257,271)(258,272);;
s2 := ( 3,195)( 4,196)( 5,217)( 6,218)( 7,219)( 8,220)( 9,209)( 10,210)
( 11,204)( 12,203)( 13,225)( 14,226)( 15,212)( 16,211)( 17,201)( 18,202)
( 19,208)( 20,207)( 21,221)( 22,222)( 23,216)( 24,215)( 25,197)( 26,198)
( 27,199)( 28,200)( 29,213)( 30,214)( 31,223)( 32,224)( 33,205)( 34,206)
( 35,163)( 36,164)( 37,185)( 38,186)( 39,187)( 40,188)( 41,177)( 42,178)
( 43,172)( 44,171)( 45,193)( 46,194)( 47,180)( 48,179)( 49,169)( 50,170)
( 51,176)( 52,175)( 53,189)( 54,190)( 55,184)( 56,183)( 57,165)( 58,166)
( 59,167)( 60,168)( 61,181)( 62,182)( 63,191)( 64,192)( 65,173)( 66,174)
( 67,291)( 68,292)( 69,313)( 70,314)( 71,315)( 72,316)( 73,305)( 74,306)
( 75,300)( 76,299)( 77,321)( 78,322)( 79,308)( 80,307)( 81,297)( 82,298)
( 83,304)( 84,303)( 85,317)( 86,318)( 87,312)( 88,311)( 89,293)( 90,294)
( 91,295)( 92,296)( 93,309)( 94,310)( 95,319)( 96,320)( 97,301)( 98,302)
( 99,259)(100,260)(101,281)(102,282)(103,283)(104,284)(105,273)(106,274)
(107,268)(108,267)(109,289)(110,290)(111,276)(112,275)(113,265)(114,266)
(115,272)(116,271)(117,285)(118,286)(119,280)(120,279)(121,261)(122,262)
(123,263)(124,264)(125,277)(126,278)(127,287)(128,288)(129,269)(130,270)
(131,227)(132,228)(133,249)(134,250)(135,251)(136,252)(137,241)(138,242)
(139,236)(140,235)(141,257)(142,258)(143,244)(144,243)(145,233)(146,234)
(147,240)(148,239)(149,253)(150,254)(151,248)(152,247)(153,229)(154,230)
(155,231)(156,232)(157,245)(158,246)(159,255)(160,256)(161,237)(162,238);;
s3 := ( 3,188)( 4,187)( 5,189)( 6,190)( 7,192)( 8,191)( 9,193)( 10,194)
( 11,180)( 12,179)( 13,181)( 14,182)( 15,184)( 16,183)( 17,185)( 18,186)
( 19,171)( 20,172)( 21,174)( 22,173)( 23,175)( 24,176)( 25,178)( 26,177)
( 27,163)( 28,164)( 29,166)( 30,165)( 31,167)( 32,168)( 33,170)( 34,169)
( 35,220)( 36,219)( 37,221)( 38,222)( 39,224)( 40,223)( 41,225)( 42,226)
( 43,212)( 44,211)( 45,213)( 46,214)( 47,216)( 48,215)( 49,217)( 50,218)
( 51,203)( 52,204)( 53,206)( 54,205)( 55,207)( 56,208)( 57,210)( 58,209)
( 59,195)( 60,196)( 61,198)( 62,197)( 63,199)( 64,200)( 65,202)( 66,201)
( 67,252)( 68,251)( 69,253)( 70,254)( 71,256)( 72,255)( 73,257)( 74,258)
( 75,244)( 76,243)( 77,245)( 78,246)( 79,248)( 80,247)( 81,249)( 82,250)
( 83,235)( 84,236)( 85,238)( 86,237)( 87,239)( 88,240)( 89,242)( 90,241)
( 91,227)( 92,228)( 93,230)( 94,229)( 95,231)( 96,232)( 97,234)( 98,233)
( 99,284)(100,283)(101,285)(102,286)(103,288)(104,287)(105,289)(106,290)
(107,276)(108,275)(109,277)(110,278)(111,280)(112,279)(113,281)(114,282)
(115,267)(116,268)(117,270)(118,269)(119,271)(120,272)(121,274)(122,273)
(123,259)(124,260)(125,262)(126,261)(127,263)(128,264)(129,266)(130,265)
(131,316)(132,315)(133,317)(134,318)(135,320)(136,319)(137,321)(138,322)
(139,308)(140,307)(141,309)(142,310)(143,312)(144,311)(145,313)(146,314)
(147,299)(148,300)(149,302)(150,301)(151,303)(152,304)(153,306)(154,305)
(155,291)(156,292)(157,294)(158,293)(159,295)(160,296)(161,298)(162,297);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(322)!(1,2);
s1 := Sym(322)!( 5, 30)( 6, 29)( 7, 17)( 8, 18)( 9, 23)( 10, 24)( 11, 20)
( 12, 19)( 13, 14)( 15, 34)( 16, 33)( 25, 31)( 26, 32)( 27, 28)( 35,131)
( 36,132)( 37,158)( 38,157)( 39,145)( 40,146)( 41,151)( 42,152)( 43,148)
( 44,147)( 45,142)( 46,141)( 47,162)( 48,161)( 49,135)( 50,136)( 51,140)
( 52,139)( 53,149)( 54,150)( 55,137)( 56,138)( 57,159)( 58,160)( 59,156)
( 60,155)( 61,134)( 62,133)( 63,153)( 64,154)( 65,144)( 66,143)( 67, 99)
( 68,100)( 69,126)( 70,125)( 71,113)( 72,114)( 73,119)( 74,120)( 75,116)
( 76,115)( 77,110)( 78,109)( 79,130)( 80,129)( 81,103)( 82,104)( 83,108)
( 84,107)( 85,117)( 86,118)( 87,105)( 88,106)( 89,127)( 90,128)( 91,124)
( 92,123)( 93,102)( 94,101)( 95,121)( 96,122)( 97,112)( 98,111)(163,164)
(165,189)(166,190)(167,178)(168,177)(169,184)(170,183)(171,179)(172,180)
(175,193)(176,194)(181,182)(185,192)(186,191)(195,292)(196,291)(197,317)
(198,318)(199,306)(200,305)(201,312)(202,311)(203,307)(204,308)(205,301)
(206,302)(207,321)(208,322)(209,296)(210,295)(211,299)(212,300)(213,310)
(214,309)(215,298)(216,297)(217,320)(218,319)(219,315)(220,316)(221,293)
(222,294)(223,314)(224,313)(225,303)(226,304)(227,260)(228,259)(229,285)
(230,286)(231,274)(232,273)(233,280)(234,279)(235,275)(236,276)(237,269)
(238,270)(239,289)(240,290)(241,264)(242,263)(243,267)(244,268)(245,278)
(246,277)(247,266)(248,265)(249,288)(250,287)(251,283)(252,284)(253,261)
(254,262)(255,282)(256,281)(257,271)(258,272);
s2 := Sym(322)!( 3,195)( 4,196)( 5,217)( 6,218)( 7,219)( 8,220)( 9,209)
( 10,210)( 11,204)( 12,203)( 13,225)( 14,226)( 15,212)( 16,211)( 17,201)
( 18,202)( 19,208)( 20,207)( 21,221)( 22,222)( 23,216)( 24,215)( 25,197)
( 26,198)( 27,199)( 28,200)( 29,213)( 30,214)( 31,223)( 32,224)( 33,205)
( 34,206)( 35,163)( 36,164)( 37,185)( 38,186)( 39,187)( 40,188)( 41,177)
( 42,178)( 43,172)( 44,171)( 45,193)( 46,194)( 47,180)( 48,179)( 49,169)
( 50,170)( 51,176)( 52,175)( 53,189)( 54,190)( 55,184)( 56,183)( 57,165)
( 58,166)( 59,167)( 60,168)( 61,181)( 62,182)( 63,191)( 64,192)( 65,173)
( 66,174)( 67,291)( 68,292)( 69,313)( 70,314)( 71,315)( 72,316)( 73,305)
( 74,306)( 75,300)( 76,299)( 77,321)( 78,322)( 79,308)( 80,307)( 81,297)
( 82,298)( 83,304)( 84,303)( 85,317)( 86,318)( 87,312)( 88,311)( 89,293)
( 90,294)( 91,295)( 92,296)( 93,309)( 94,310)( 95,319)( 96,320)( 97,301)
( 98,302)( 99,259)(100,260)(101,281)(102,282)(103,283)(104,284)(105,273)
(106,274)(107,268)(108,267)(109,289)(110,290)(111,276)(112,275)(113,265)
(114,266)(115,272)(116,271)(117,285)(118,286)(119,280)(120,279)(121,261)
(122,262)(123,263)(124,264)(125,277)(126,278)(127,287)(128,288)(129,269)
(130,270)(131,227)(132,228)(133,249)(134,250)(135,251)(136,252)(137,241)
(138,242)(139,236)(140,235)(141,257)(142,258)(143,244)(144,243)(145,233)
(146,234)(147,240)(148,239)(149,253)(150,254)(151,248)(152,247)(153,229)
(154,230)(155,231)(156,232)(157,245)(158,246)(159,255)(160,256)(161,237)
(162,238);
s3 := Sym(322)!( 3,188)( 4,187)( 5,189)( 6,190)( 7,192)( 8,191)( 9,193)
( 10,194)( 11,180)( 12,179)( 13,181)( 14,182)( 15,184)( 16,183)( 17,185)
( 18,186)( 19,171)( 20,172)( 21,174)( 22,173)( 23,175)( 24,176)( 25,178)
( 26,177)( 27,163)( 28,164)( 29,166)( 30,165)( 31,167)( 32,168)( 33,170)
( 34,169)( 35,220)( 36,219)( 37,221)( 38,222)( 39,224)( 40,223)( 41,225)
( 42,226)( 43,212)( 44,211)( 45,213)( 46,214)( 47,216)( 48,215)( 49,217)
( 50,218)( 51,203)( 52,204)( 53,206)( 54,205)( 55,207)( 56,208)( 57,210)
( 58,209)( 59,195)( 60,196)( 61,198)( 62,197)( 63,199)( 64,200)( 65,202)
( 66,201)( 67,252)( 68,251)( 69,253)( 70,254)( 71,256)( 72,255)( 73,257)
( 74,258)( 75,244)( 76,243)( 77,245)( 78,246)( 79,248)( 80,247)( 81,249)
( 82,250)( 83,235)( 84,236)( 85,238)( 86,237)( 87,239)( 88,240)( 89,242)
( 90,241)( 91,227)( 92,228)( 93,230)( 94,229)( 95,231)( 96,232)( 97,234)
( 98,233)( 99,284)(100,283)(101,285)(102,286)(103,288)(104,287)(105,289)
(106,290)(107,276)(108,275)(109,277)(110,278)(111,280)(112,279)(113,281)
(114,282)(115,267)(116,268)(117,270)(118,269)(119,271)(120,272)(121,274)
(122,273)(123,259)(124,260)(125,262)(126,261)(127,263)(128,264)(129,266)
(130,265)(131,316)(132,315)(133,317)(134,318)(135,320)(136,319)(137,321)
(138,322)(139,308)(140,307)(141,309)(142,310)(143,312)(144,311)(145,313)
(146,314)(147,299)(148,300)(149,302)(150,301)(151,303)(152,304)(153,306)
(154,305)(155,291)(156,292)(157,294)(158,293)(159,295)(160,296)(161,298)
(162,297);
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, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope