Polytope of Type {201,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {201,4}*1608
if this polytope has a name.
Group : SmallGroup(1608,43)
Rank : 3
Schlafli Type : {201,4}
Number of vertices, edges, etc : 201, 402, 4
Order of s0s1s2 : 201
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   67-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

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

Twisty Puzzle