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