Polytope of Type {20,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8}*640a
if this polytope has a name.
Group : SmallGroup(640,1159)
Rank : 3
Schlafli Type : {20,8}
Number of vertices, edges, etc : 40, 160, 16
Order of s0s1s2 : 40
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,8,2} of size 1280
Vertex Figure Of :
   {2,20,8} of size 1280
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,4}*320, {20,8}*320a, {20,8}*320b
   4-fold quotients : {20,4}*160, {10,8}*160
   5-fold quotients : {4,8}*128a
   8-fold quotients : {20,2}*80, {10,4}*80
   10-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
   16-fold quotients : {10,2}*40
   20-fold quotients : {4,4}*32, {2,8}*32
   32-fold quotients : {5,2}*20
   40-fold quotients : {2,4}*16, {4,2}*16
   80-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {40,8}*1280a, {20,8}*1280a, {40,8}*1280c, {20,16}*1280a, {20,16}*1280b
   3-fold covers : {60,8}*1920a, {20,24}*1920a
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 2.
      12 facets:
         8 of {10}*20
         4 of {20}*40
      20 vertex figures:
         20 of {8}*16

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

Twisty Puzzle