Polytope of Type {4,159}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,159}*1272
if this polytope has a name.
Group : SmallGroup(1272,35)
Rank : 3
Schlafli Type : {4,159}
Number of vertices, edges, etc : 4, 318, 159
Order of s₀s₁s₂ : 159
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) :
   53-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);;
s1 := (  3,  4)(  5,209)(  6,210)(  7,212)(  8,211)(  9,205)( 10,206)( 11,208)
( 12,207)( 13,201)( 14,202)( 15,204)( 16,203)( 17,197)( 18,198)( 19,200)
( 20,199)( 21,193)( 22,194)( 23,196)( 24,195)( 25,189)( 26,190)( 27,192)
( 28,191)( 29,185)( 30,186)( 31,188)( 32,187)( 33,181)( 34,182)( 35,184)
( 36,183)( 37,177)( 38,178)( 39,180)( 40,179)( 41,173)( 42,174)( 43,176)
( 44,175)( 45,169)( 46,170)( 47,172)( 48,171)( 49,165)( 50,166)( 51,168)
( 52,167)( 53,161)( 54,162)( 55,164)( 56,163)( 57,157)( 58,158)( 59,160)
( 60,159)( 61,153)( 62,154)( 63,156)( 64,155)( 65,149)( 66,150)( 67,152)
( 68,151)( 69,145)( 70,146)( 71,148)( 72,147)( 73,141)( 74,142)( 75,144)
( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,133)( 82,134)( 83,136)
( 84,135)( 85,129)( 86,130)( 87,132)( 88,131)( 89,125)( 90,126)( 91,128)
( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)( 97,117)( 98,118)( 99,120)
(100,119)(101,113)(102,114)(103,116)(104,115)(105,109)(106,110)(107,112)
(108,111);;
s2 := (  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9,209)( 10,212)( 11,211)( 12,210)
( 13,205)( 14,208)( 15,207)( 16,206)( 17,201)( 18,204)( 19,203)( 20,202)
( 21,197)( 22,200)( 23,199)( 24,198)( 25,193)( 26,196)( 27,195)( 28,194)
( 29,189)( 30,192)( 31,191)( 32,190)( 33,185)( 34,188)( 35,187)( 36,186)
( 37,181)( 38,184)( 39,183)( 40,182)( 41,177)( 42,180)( 43,179)( 44,178)
( 45,173)( 46,176)( 47,175)( 48,174)( 49,169)( 50,172)( 51,171)( 52,170)
( 53,165)( 54,168)( 55,167)( 56,166)( 57,161)( 58,164)( 59,163)( 60,162)
( 61,157)( 62,160)( 63,159)( 64,158)( 65,153)( 66,156)( 67,155)( 68,154)
( 69,149)( 70,152)( 71,151)( 72,150)( 73,145)( 74,148)( 75,147)( 76,146)
( 77,141)( 78,144)( 79,143)( 80,142)( 81,137)( 82,140)( 83,139)( 84,138)
( 85,133)( 86,136)( 87,135)( 88,134)( 89,129)( 90,132)( 91,131)( 92,130)
( 93,125)( 94,128)( 95,127)( 96,126)( 97,121)( 98,124)( 99,123)(100,122)
(101,117)(102,120)(103,119)(104,118)(105,113)(106,116)(107,115)(108,114)
(110,112);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(212)!(  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);
s1 := Sym(212)!(  3,  4)(  5,209)(  6,210)(  7,212)(  8,211)(  9,205)( 10,206)
( 11,208)( 12,207)( 13,201)( 14,202)( 15,204)( 16,203)( 17,197)( 18,198)
( 19,200)( 20,199)( 21,193)( 22,194)( 23,196)( 24,195)( 25,189)( 26,190)
( 27,192)( 28,191)( 29,185)( 30,186)( 31,188)( 32,187)( 33,181)( 34,182)
( 35,184)( 36,183)( 37,177)( 38,178)( 39,180)( 40,179)( 41,173)( 42,174)
( 43,176)( 44,175)( 45,169)( 46,170)( 47,172)( 48,171)( 49,165)( 50,166)
( 51,168)( 52,167)( 53,161)( 54,162)( 55,164)( 56,163)( 57,157)( 58,158)
( 59,160)( 60,159)( 61,153)( 62,154)( 63,156)( 64,155)( 65,149)( 66,150)
( 67,152)( 68,151)( 69,145)( 70,146)( 71,148)( 72,147)( 73,141)( 74,142)
( 75,144)( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,133)( 82,134)
( 83,136)( 84,135)( 85,129)( 86,130)( 87,132)( 88,131)( 89,125)( 90,126)
( 91,128)( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)( 97,117)( 98,118)
( 99,120)(100,119)(101,113)(102,114)(103,116)(104,115)(105,109)(106,110)
(107,112)(108,111);
s2 := Sym(212)!(  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9,209)( 10,212)( 11,211)
( 12,210)( 13,205)( 14,208)( 15,207)( 16,206)( 17,201)( 18,204)( 19,203)
( 20,202)( 21,197)( 22,200)( 23,199)( 24,198)( 25,193)( 26,196)( 27,195)
( 28,194)( 29,189)( 30,192)( 31,191)( 32,190)( 33,185)( 34,188)( 35,187)
( 36,186)( 37,181)( 38,184)( 39,183)( 40,182)( 41,177)( 42,180)( 43,179)
( 44,178)( 45,173)( 46,176)( 47,175)( 48,174)( 49,169)( 50,172)( 51,171)
( 52,170)( 53,165)( 54,168)( 55,167)( 56,166)( 57,161)( 58,164)( 59,163)
( 60,162)( 61,157)( 62,160)( 63,159)( 64,158)( 65,153)( 66,156)( 67,155)
( 68,154)( 69,149)( 70,152)( 71,151)( 72,150)( 73,145)( 74,148)( 75,147)
( 76,146)( 77,141)( 78,144)( 79,143)( 80,142)( 81,137)( 82,140)( 83,139)
( 84,138)( 85,133)( 86,136)( 87,135)( 88,134)( 89,129)( 90,132)( 91,131)
( 92,130)( 93,125)( 94,128)( 95,127)( 96,126)( 97,121)( 98,124)( 99,123)
(100,122)(101,117)(102,120)(103,119)(104,118)(105,113)(106,116)(107,115)
(108,114)(110,112);
poly := sub<Sym(212)|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 >;

References : None.
to this polytope