Polytope of Type {12,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,10}*1200b
if this polytope has a name.
Group : SmallGroup(1200,514)
Rank : 3
Schlafli Type : {12,10}
Number of vertices, edges, etc : 60, 300, 50
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,10}*600a
   4-fold quotients : {6,10}*300
   25-fold quotients : {12,2}*48
   50-fold quotients : {6,2}*24
   75-fold quotients : {4,2}*16
   100-fold quotients : {3,2}*12
   150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 5.
      10 facets:
         10 of {12}*24
      12 vertex figures:
         12 of {10}*20
   P/N, where N=<s1*s2*s1*s2> of order 5.
      10 facets:
         10 of {12}*24
      28 vertex figures:
         20 of {2}*4
         8 of {10}*20

Permutation Representation (GAP) :

s0 := (  2,  5)(  3,  4)(  6,  7)(  8, 10)( 11, 13)( 14, 15)( 16, 19)( 17, 18)( 21, 25)( 22, 24)( 26, 51)( 27, 55)( 28, 54)( 29, 53)( 30, 52)( 31, 57)( 32, 56)( 33, 60)( 34, 59)( 35, 58)( 36, 63)( 37, 62)( 38, 61)( 39, 65)( 40, 64)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 70)( 46, 75)( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 77, 80)( 78, 79)( 81, 82)( 83, 85)( 86, 88)( 89, 90)( 91, 94)( 92, 93)( 96,100)( 97, 99)(101,126)(102,130)(103,129)(104,128)(105,127)(106,132)(107,131)(108,135)(109,134)(110,133)(111,138)(112,137)(113,136)(114,140)(115,139)(116,144)(117,143)(118,142)(119,141)(120,145)(121,150)(122,149)(123,148)(124,147)(125,146)(151,226)(152,230)(153,229)(154,228)(155,227)(156,232)(157,231)(158,235)(159,234)(160,233)(161,238)(162,237)(163,236)(164,240)(165,239)(166,244)(167,243)(168,242)(169,241)(170,245)(171,250)(172,249)(173,248)(174,247)(175,246)(176,276)(177,280)(178,279)(179,278)(180,277)(181,282)(182,281)(183,285)(184,284)(185,283)(186,288)(187,287)(188,286)(189,290)(190,289)(191,294)(192,293)(193,292)(194,291)(195,295)(196,300)(197,299)(198,298)(199,297)(200,296)(201,251)(202,255)(203,254)(204,253)(205,252)(206,257)(207,256)(208,260)(209,259)(210,258)(211,263)(212,262)(213,261)(214,265)(215,264)(216,269)(217,268)(218,267)(219,266)(220,270)(221,275)(222,274)(223,273)(224,272)(225,271);;
s1 := (  1,176)(  2,200)(  3,194)(  4,188)(  5,182)(  6,181)(  7,180)(  8,199)(  9,193)( 10,187)( 11,186)( 12,185)( 13,179)( 14,198)( 15,192)( 16,191)( 17,190)( 18,184)( 19,178)( 20,197)( 21,196)( 22,195)( 23,189)( 24,183)( 25,177)( 26,151)( 27,175)( 28,169)( 29,163)( 30,157)( 31,156)( 32,155)( 33,174)( 34,168)( 35,162)( 36,161)( 37,160)( 38,154)( 39,173)( 40,167)( 41,166)( 42,165)( 43,159)( 44,153)( 45,172)( 46,171)( 47,170)( 48,164)( 49,158)( 50,152)( 51,201)( 52,225)( 53,219)( 54,213)( 55,207)( 56,206)( 57,205)( 58,224)( 59,218)( 60,212)( 61,211)( 62,210)( 63,204)( 64,223)( 65,217)( 66,216)( 67,215)( 68,209)( 69,203)( 70,222)( 71,221)( 72,220)( 73,214)( 74,208)( 75,202)( 76,251)( 77,275)( 78,269)( 79,263)( 80,257)( 81,256)( 82,255)( 83,274)( 84,268)( 85,262)( 86,261)( 87,260)( 88,254)( 89,273)( 90,267)( 91,266)( 92,265)( 93,259)( 94,253)( 95,272)( 96,271)( 97,270)( 98,264)( 99,258)(100,252)(101,226)(102,250)(103,244)(104,238)(105,232)(106,231)(107,230)(108,249)(109,243)(110,237)(111,236)(112,235)(113,229)(114,248)(115,242)(116,241)(117,240)(118,234)(119,228)(120,247)(121,246)(122,245)(123,239)(124,233)(125,227)(126,276)(127,300)(128,294)(129,288)(130,282)(131,281)(132,280)(133,299)(134,293)(135,287)(136,286)(137,285)(138,279)(139,298)(140,292)(141,291)(142,290)(143,284)(144,278)(145,297)(146,296)(147,295)(148,289)(149,283)(150,277);;
s2 := (  1, 12)(  2, 11)(  3, 15)(  4, 14)(  5, 13)(  6,  7)(  8, 10)( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 37)( 27, 36)( 28, 40)( 29, 39)( 30, 38)( 31, 32)( 33, 35)( 41, 47)( 42, 46)( 43, 50)( 44, 49)( 45, 48)( 51, 62)( 52, 61)( 53, 65)( 54, 64)( 55, 63)( 56, 57)( 58, 60)( 66, 72)( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 87)( 77, 86)( 78, 90)( 79, 89)( 80, 88)( 81, 82)( 83, 85)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)(101,112)(102,111)(103,115)(104,114)(105,113)(106,107)(108,110)(116,122)(117,121)(118,125)(119,124)(120,123)(126,137)(127,136)(128,140)(129,139)(130,138)(131,132)(133,135)(141,147)(142,146)(143,150)(144,149)(145,148)(151,162)(152,161)(153,165)(154,164)(155,163)(156,157)(158,160)(166,172)(167,171)(168,175)(169,174)(170,173)(176,187)(177,186)(178,190)(179,189)(180,188)(181,182)(183,185)(191,197)(192,196)(193,200)(194,199)(195,198)(201,212)(202,211)(203,215)(204,214)(205,213)(206,207)(208,210)(216,222)(217,221)(218,225)(219,224)(220,223)(226,237)(227,236)(228,240)(229,239)(230,238)(231,232)(233,235)(241,247)(242,246)(243,250)(244,249)(245,248)(251,262)(252,261)(253,265)(254,264)(255,263)(256,257)(258,260)(266,272)(267,271)(268,275)(269,274)(270,273)(276,287)(277,286)(278,290)(279,289)(280,288)(281,282)(283,285)(291,297)(292,296)(293,300)(294,299)(295,298);;
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*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(300)!(  2,  5)(  3,  4)(  6,  7)(  8, 10)( 11, 13)( 14, 15)( 16, 19)( 17, 18)( 21, 25)( 22, 24)( 26, 51)( 27, 55)( 28, 54)( 29, 53)( 30, 52)( 31, 57)( 32, 56)( 33, 60)( 34, 59)( 35, 58)( 36, 63)( 37, 62)( 38, 61)( 39, 65)( 40, 64)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 70)( 46, 75)( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 77, 80)( 78, 79)( 81, 82)( 83, 85)( 86, 88)( 89, 90)( 91, 94)( 92, 93)( 96,100)( 97, 99)(101,126)(102,130)(103,129)(104,128)(105,127)(106,132)(107,131)(108,135)(109,134)(110,133)(111,138)(112,137)(113,136)(114,140)(115,139)(116,144)(117,143)(118,142)(119,141)(120,145)(121,150)(122,149)(123,148)(124,147)(125,146)(151,226)(152,230)(153,229)(154,228)(155,227)(156,232)(157,231)(158,235)(159,234)(160,233)(161,238)(162,237)(163,236)(164,240)(165,239)(166,244)(167,243)(168,242)(169,241)(170,245)(171,250)(172,249)(173,248)(174,247)(175,246)(176,276)(177,280)(178,279)(179,278)(180,277)(181,282)(182,281)(183,285)(184,284)(185,283)(186,288)(187,287)(188,286)(189,290)(190,289)(191,294)(192,293)(193,292)(194,291)(195,295)(196,300)(197,299)(198,298)(199,297)(200,296)(201,251)(202,255)(203,254)(204,253)(205,252)(206,257)(207,256)(208,260)(209,259)(210,258)(211,263)(212,262)(213,261)(214,265)(215,264)(216,269)(217,268)(218,267)(219,266)(220,270)(221,275)(222,274)(223,273)(224,272)(225,271);
s1 := Sym(300)!(  1,176)(  2,200)(  3,194)(  4,188)(  5,182)(  6,181)(  7,180)(  8,199)(  9,193)( 10,187)( 11,186)( 12,185)( 13,179)( 14,198)( 15,192)( 16,191)( 17,190)( 18,184)( 19,178)( 20,197)( 21,196)( 22,195)( 23,189)( 24,183)( 25,177)( 26,151)( 27,175)( 28,169)( 29,163)( 30,157)( 31,156)( 32,155)( 33,174)( 34,168)( 35,162)( 36,161)( 37,160)( 38,154)( 39,173)( 40,167)( 41,166)( 42,165)( 43,159)( 44,153)( 45,172)( 46,171)( 47,170)( 48,164)( 49,158)( 50,152)( 51,201)( 52,225)( 53,219)( 54,213)( 55,207)( 56,206)( 57,205)( 58,224)( 59,218)( 60,212)( 61,211)( 62,210)( 63,204)( 64,223)( 65,217)( 66,216)( 67,215)( 68,209)( 69,203)( 70,222)( 71,221)( 72,220)( 73,214)( 74,208)( 75,202)( 76,251)( 77,275)( 78,269)( 79,263)( 80,257)( 81,256)( 82,255)( 83,274)( 84,268)( 85,262)( 86,261)( 87,260)( 88,254)( 89,273)( 90,267)( 91,266)( 92,265)( 93,259)( 94,253)( 95,272)( 96,271)( 97,270)( 98,264)( 99,258)(100,252)(101,226)(102,250)(103,244)(104,238)(105,232)(106,231)(107,230)(108,249)(109,243)(110,237)(111,236)(112,235)(113,229)(114,248)(115,242)(116,241)(117,240)(118,234)(119,228)(120,247)(121,246)(122,245)(123,239)(124,233)(125,227)(126,276)(127,300)(128,294)(129,288)(130,282)(131,281)(132,280)(133,299)(134,293)(135,287)(136,286)(137,285)(138,279)(139,298)(140,292)(141,291)(142,290)(143,284)(144,278)(145,297)(146,296)(147,295)(148,289)(149,283)(150,277);
s2 := Sym(300)!(  1, 12)(  2, 11)(  3, 15)(  4, 14)(  5, 13)(  6,  7)(  8, 10)( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 37)( 27, 36)( 28, 40)( 29, 39)( 30, 38)( 31, 32)( 33, 35)( 41, 47)( 42, 46)( 43, 50)( 44, 49)( 45, 48)( 51, 62)( 52, 61)( 53, 65)( 54, 64)( 55, 63)( 56, 57)( 58, 60)( 66, 72)( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 87)( 77, 86)( 78, 90)( 79, 89)( 80, 88)( 81, 82)( 83, 85)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)(101,112)(102,111)(103,115)(104,114)(105,113)(106,107)(108,110)(116,122)(117,121)(118,125)(119,124)(120,123)(126,137)(127,136)(128,140)(129,139)(130,138)(131,132)(133,135)(141,147)(142,146)(143,150)(144,149)(145,148)(151,162)(152,161)(153,165)(154,164)(155,163)(156,157)(158,160)(166,172)(167,171)(168,175)(169,174)(170,173)(176,187)(177,186)(178,190)(179,189)(180,188)(181,182)(183,185)(191,197)(192,196)(193,200)(194,199)(195,198)(201,212)(202,211)(203,215)(204,214)(205,213)(206,207)(208,210)(216,222)(217,221)(218,225)(219,224)(220,223)(226,237)(227,236)(228,240)(229,239)(230,238)(231,232)(233,235)(241,247)(242,246)(243,250)(244,249)(245,248)(251,262)(252,261)(253,265)(254,264)(255,263)(256,257)(258,260)(266,272)(267,271)(268,275)(269,274)(270,273)(276,287)(277,286)(278,290)(279,289)(280,288)(281,282)(283,285)(291,297)(292,296)(293,300)(294,299)(295,298);
poly := sub<Sym(300)|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*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*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 >;

References : None.
to this polytope

Polytope of Type {12,10}

Twisty Puzzle