Polytope of Type {4,201}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope