Polytope of Type {10,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10}*640d
if this polytope has a name.
Group : SmallGroup(640,21537)
Rank : 3
Schlafli Type : {10,10}
Number of vertices, edges, etc : 32, 160, 32
Order of s0s1s2 : 4
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {10,10,2} of size 1280
Vertex Figure Of :
   {2,10,10} of size 1280
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,10}*320b, {10,5}*320b
   4-fold quotients : {5,5}*160
   80-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,20}*1280c, {20,10}*1280c, {10,10}*1280a, {10,20}*1280d, {10,20}*1280e, {20,10}*1280d, {20,10}*1280e, {10,10}*1280b, {10,10}*1280c, {10,20}*1280f, {20,10}*1280f
   3-fold covers : {10,30}*1920b, {30,10}*1920b
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      16 facets:
         16 of {10}*20
      16 vertex figures:
         16 of {10}*20
   P/N, where N=<s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 2.
      16 facets:
         16 of {10}*20
      16 vertex figures:
         16 of {10}*20
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1> of order 2.
      16 facets:
         16 of {10}*20
      16 vertex figures:
         16 of {10}*20
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s1*s2*s1> of order 2.
      16 facets:
         16 of {10}*20
      16 vertex figures:
         16 of {10}*20

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

Twisty Puzzle