Polytope of Type {20,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,5}*640a
if this polytope has a name.
Group : SmallGroup(640,21465)
Rank : 3
Schlafli Type : {20,5}
Number of vertices, edges, etc : 64, 160, 16
Order of s0s1s2 : 8
Order of s0s1s2s1 : 20
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{20,5,2} of size 1280
Vertex Figure Of :
{2,20,5} of size 1280
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,5}*320b
4-fold quotients : {5,5}*160
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,5}*1280, {20,10}*1280b, {20,10}*1280e
3-fold covers : {20,15}*1920a
Permutation Representation (GAP) :
s0 := ( 3, 28)( 4, 27)( 5, 15)( 6, 16)( 7, 21)( 8, 22)( 9, 18)( 10, 17)
( 11, 12)( 13, 32)( 14, 31)( 23, 29)( 24, 30)( 25, 26)( 33,129)( 34,130)
( 35,156)( 36,155)( 37,143)( 38,144)( 39,149)( 40,150)( 41,146)( 42,145)
( 43,140)( 44,139)( 45,160)( 46,159)( 47,133)( 48,134)( 49,138)( 50,137)
( 51,147)( 52,148)( 53,135)( 54,136)( 55,157)( 56,158)( 57,154)( 58,153)
( 59,132)( 60,131)( 61,151)( 62,152)( 63,142)( 64,141)( 65, 97)( 66, 98)
( 67,124)( 68,123)( 69,111)( 70,112)( 71,117)( 72,118)( 73,114)( 74,113)
( 75,108)( 76,107)( 77,128)( 78,127)( 79,101)( 80,102)( 81,106)( 82,105)
( 83,115)( 84,116)( 85,103)( 86,104)( 87,125)( 88,126)( 89,122)( 90,121)
( 91,100)( 92, 99)( 93,119)( 94,120)( 95,110)( 96,109)(161,162)(163,187)
(164,188)(165,176)(166,175)(167,182)(168,181)(169,177)(170,178)(173,191)
(174,192)(179,180)(183,190)(184,189)(193,290)(194,289)(195,315)(196,316)
(197,304)(198,303)(199,310)(200,309)(201,305)(202,306)(203,299)(204,300)
(205,319)(206,320)(207,294)(208,293)(209,297)(210,298)(211,308)(212,307)
(213,296)(214,295)(215,318)(216,317)(217,313)(218,314)(219,291)(220,292)
(221,312)(222,311)(223,301)(224,302)(225,258)(226,257)(227,283)(228,284)
(229,272)(230,271)(231,278)(232,277)(233,273)(234,274)(235,267)(236,268)
(237,287)(238,288)(239,262)(240,261)(241,265)(242,266)(243,276)(244,275)
(245,264)(246,263)(247,286)(248,285)(249,281)(250,282)(251,259)(252,260)
(253,280)(254,279)(255,269)(256,270);;
s1 := ( 1,193)( 2,194)( 3,215)( 4,216)( 5,217)( 6,218)( 7,207)( 8,208)
( 9,202)( 10,201)( 11,223)( 12,224)( 13,210)( 14,209)( 15,199)( 16,200)
( 17,206)( 18,205)( 19,219)( 20,220)( 21,214)( 22,213)( 23,195)( 24,196)
( 25,197)( 26,198)( 27,211)( 28,212)( 29,221)( 30,222)( 31,203)( 32,204)
( 33,161)( 34,162)( 35,183)( 36,184)( 37,185)( 38,186)( 39,175)( 40,176)
( 41,170)( 42,169)( 43,191)( 44,192)( 45,178)( 46,177)( 47,167)( 48,168)
( 49,174)( 50,173)( 51,187)( 52,188)( 53,182)( 54,181)( 55,163)( 56,164)
( 57,165)( 58,166)( 59,179)( 60,180)( 61,189)( 62,190)( 63,171)( 64,172)
( 65,289)( 66,290)( 67,311)( 68,312)( 69,313)( 70,314)( 71,303)( 72,304)
( 73,298)( 74,297)( 75,319)( 76,320)( 77,306)( 78,305)( 79,295)( 80,296)
( 81,302)( 82,301)( 83,315)( 84,316)( 85,310)( 86,309)( 87,291)( 88,292)
( 89,293)( 90,294)( 91,307)( 92,308)( 93,317)( 94,318)( 95,299)( 96,300)
( 97,257)( 98,258)( 99,279)(100,280)(101,281)(102,282)(103,271)(104,272)
(105,266)(106,265)(107,287)(108,288)(109,274)(110,273)(111,263)(112,264)
(113,270)(114,269)(115,283)(116,284)(117,278)(118,277)(119,259)(120,260)
(121,261)(122,262)(123,275)(124,276)(125,285)(126,286)(127,267)(128,268)
(129,225)(130,226)(131,247)(132,248)(133,249)(134,250)(135,239)(136,240)
(137,234)(138,233)(139,255)(140,256)(141,242)(142,241)(143,231)(144,232)
(145,238)(146,237)(147,251)(148,252)(149,246)(150,245)(151,227)(152,228)
(153,229)(154,230)(155,243)(156,244)(157,253)(158,254)(159,235)(160,236);;
s2 := ( 1,172)( 2,171)( 3,178)( 4,177)( 5,166)( 6,165)( 7,191)( 8,192)
( 9,187)( 10,188)( 11,162)( 12,161)( 13,181)( 14,182)( 15,175)( 16,176)
( 17,164)( 18,163)( 19,186)( 20,185)( 21,173)( 22,174)( 23,184)( 24,183)
( 25,180)( 26,179)( 27,169)( 28,170)( 29,189)( 30,190)( 31,167)( 32,168)
( 33,300)( 34,299)( 35,306)( 36,305)( 37,294)( 38,293)( 39,319)( 40,320)
( 41,315)( 42,316)( 43,290)( 44,289)( 45,309)( 46,310)( 47,303)( 48,304)
( 49,292)( 50,291)( 51,314)( 52,313)( 53,301)( 54,302)( 55,312)( 56,311)
( 57,308)( 58,307)( 59,297)( 60,298)( 61,317)( 62,318)( 63,295)( 64,296)
( 65,268)( 66,267)( 67,274)( 68,273)( 69,262)( 70,261)( 71,287)( 72,288)
( 73,283)( 74,284)( 75,258)( 76,257)( 77,277)( 78,278)( 79,271)( 80,272)
( 81,260)( 82,259)( 83,282)( 84,281)( 85,269)( 86,270)( 87,280)( 88,279)
( 89,276)( 90,275)( 91,265)( 92,266)( 93,285)( 94,286)( 95,263)( 96,264)
( 97,236)( 98,235)( 99,242)(100,241)(101,230)(102,229)(103,255)(104,256)
(105,251)(106,252)(107,226)(108,225)(109,245)(110,246)(111,239)(112,240)
(113,228)(114,227)(115,250)(116,249)(117,237)(118,238)(119,248)(120,247)
(121,244)(122,243)(123,233)(124,234)(125,253)(126,254)(127,231)(128,232)
(129,204)(130,203)(131,210)(132,209)(133,198)(134,197)(135,223)(136,224)
(137,219)(138,220)(139,194)(140,193)(141,213)(142,214)(143,207)(144,208)
(145,196)(146,195)(147,218)(148,217)(149,205)(150,206)(151,216)(152,215)
(153,212)(154,211)(155,201)(156,202)(157,221)(158,222)(159,199)(160,200);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(320)!( 3, 28)( 4, 27)( 5, 15)( 6, 16)( 7, 21)( 8, 22)( 9, 18)
( 10, 17)( 11, 12)( 13, 32)( 14, 31)( 23, 29)( 24, 30)( 25, 26)( 33,129)
( 34,130)( 35,156)( 36,155)( 37,143)( 38,144)( 39,149)( 40,150)( 41,146)
( 42,145)( 43,140)( 44,139)( 45,160)( 46,159)( 47,133)( 48,134)( 49,138)
( 50,137)( 51,147)( 52,148)( 53,135)( 54,136)( 55,157)( 56,158)( 57,154)
( 58,153)( 59,132)( 60,131)( 61,151)( 62,152)( 63,142)( 64,141)( 65, 97)
( 66, 98)( 67,124)( 68,123)( 69,111)( 70,112)( 71,117)( 72,118)( 73,114)
( 74,113)( 75,108)( 76,107)( 77,128)( 78,127)( 79,101)( 80,102)( 81,106)
( 82,105)( 83,115)( 84,116)( 85,103)( 86,104)( 87,125)( 88,126)( 89,122)
( 90,121)( 91,100)( 92, 99)( 93,119)( 94,120)( 95,110)( 96,109)(161,162)
(163,187)(164,188)(165,176)(166,175)(167,182)(168,181)(169,177)(170,178)
(173,191)(174,192)(179,180)(183,190)(184,189)(193,290)(194,289)(195,315)
(196,316)(197,304)(198,303)(199,310)(200,309)(201,305)(202,306)(203,299)
(204,300)(205,319)(206,320)(207,294)(208,293)(209,297)(210,298)(211,308)
(212,307)(213,296)(214,295)(215,318)(216,317)(217,313)(218,314)(219,291)
(220,292)(221,312)(222,311)(223,301)(224,302)(225,258)(226,257)(227,283)
(228,284)(229,272)(230,271)(231,278)(232,277)(233,273)(234,274)(235,267)
(236,268)(237,287)(238,288)(239,262)(240,261)(241,265)(242,266)(243,276)
(244,275)(245,264)(246,263)(247,286)(248,285)(249,281)(250,282)(251,259)
(252,260)(253,280)(254,279)(255,269)(256,270);
s1 := Sym(320)!( 1,193)( 2,194)( 3,215)( 4,216)( 5,217)( 6,218)( 7,207)
( 8,208)( 9,202)( 10,201)( 11,223)( 12,224)( 13,210)( 14,209)( 15,199)
( 16,200)( 17,206)( 18,205)( 19,219)( 20,220)( 21,214)( 22,213)( 23,195)
( 24,196)( 25,197)( 26,198)( 27,211)( 28,212)( 29,221)( 30,222)( 31,203)
( 32,204)( 33,161)( 34,162)( 35,183)( 36,184)( 37,185)( 38,186)( 39,175)
( 40,176)( 41,170)( 42,169)( 43,191)( 44,192)( 45,178)( 46,177)( 47,167)
( 48,168)( 49,174)( 50,173)( 51,187)( 52,188)( 53,182)( 54,181)( 55,163)
( 56,164)( 57,165)( 58,166)( 59,179)( 60,180)( 61,189)( 62,190)( 63,171)
( 64,172)( 65,289)( 66,290)( 67,311)( 68,312)( 69,313)( 70,314)( 71,303)
( 72,304)( 73,298)( 74,297)( 75,319)( 76,320)( 77,306)( 78,305)( 79,295)
( 80,296)( 81,302)( 82,301)( 83,315)( 84,316)( 85,310)( 86,309)( 87,291)
( 88,292)( 89,293)( 90,294)( 91,307)( 92,308)( 93,317)( 94,318)( 95,299)
( 96,300)( 97,257)( 98,258)( 99,279)(100,280)(101,281)(102,282)(103,271)
(104,272)(105,266)(106,265)(107,287)(108,288)(109,274)(110,273)(111,263)
(112,264)(113,270)(114,269)(115,283)(116,284)(117,278)(118,277)(119,259)
(120,260)(121,261)(122,262)(123,275)(124,276)(125,285)(126,286)(127,267)
(128,268)(129,225)(130,226)(131,247)(132,248)(133,249)(134,250)(135,239)
(136,240)(137,234)(138,233)(139,255)(140,256)(141,242)(142,241)(143,231)
(144,232)(145,238)(146,237)(147,251)(148,252)(149,246)(150,245)(151,227)
(152,228)(153,229)(154,230)(155,243)(156,244)(157,253)(158,254)(159,235)
(160,236);
s2 := Sym(320)!( 1,172)( 2,171)( 3,178)( 4,177)( 5,166)( 6,165)( 7,191)
( 8,192)( 9,187)( 10,188)( 11,162)( 12,161)( 13,181)( 14,182)( 15,175)
( 16,176)( 17,164)( 18,163)( 19,186)( 20,185)( 21,173)( 22,174)( 23,184)
( 24,183)( 25,180)( 26,179)( 27,169)( 28,170)( 29,189)( 30,190)( 31,167)
( 32,168)( 33,300)( 34,299)( 35,306)( 36,305)( 37,294)( 38,293)( 39,319)
( 40,320)( 41,315)( 42,316)( 43,290)( 44,289)( 45,309)( 46,310)( 47,303)
( 48,304)( 49,292)( 50,291)( 51,314)( 52,313)( 53,301)( 54,302)( 55,312)
( 56,311)( 57,308)( 58,307)( 59,297)( 60,298)( 61,317)( 62,318)( 63,295)
( 64,296)( 65,268)( 66,267)( 67,274)( 68,273)( 69,262)( 70,261)( 71,287)
( 72,288)( 73,283)( 74,284)( 75,258)( 76,257)( 77,277)( 78,278)( 79,271)
( 80,272)( 81,260)( 82,259)( 83,282)( 84,281)( 85,269)( 86,270)( 87,280)
( 88,279)( 89,276)( 90,275)( 91,265)( 92,266)( 93,285)( 94,286)( 95,263)
( 96,264)( 97,236)( 98,235)( 99,242)(100,241)(101,230)(102,229)(103,255)
(104,256)(105,251)(106,252)(107,226)(108,225)(109,245)(110,246)(111,239)
(112,240)(113,228)(114,227)(115,250)(116,249)(117,237)(118,238)(119,248)
(120,247)(121,244)(122,243)(123,233)(124,234)(125,253)(126,254)(127,231)
(128,232)(129,204)(130,203)(131,210)(132,209)(133,198)(134,197)(135,223)
(136,224)(137,219)(138,220)(139,194)(140,193)(141,213)(142,214)(143,207)
(144,208)(145,196)(146,195)(147,218)(148,217)(149,205)(150,206)(151,216)
(152,215)(153,212)(154,211)(155,201)(156,202)(157,221)(158,222)(159,199)
(160,200);
poly := sub<Sym(320)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1 >;
References : None.
to this polytope