Polytope of Type {20,5}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,5}*640b
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 : 4
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}*1280a, {20,10}*1280d
   3-fold covers : {20,15}*1920b
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      8 facets:
         8 of {20}*40
      32 vertex figures:
         32 of {5}*10

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

Twisty Puzzle