Polytope of Type {159,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {159,4}*1272
if this polytope has a name.
Group : SmallGroup(1272,35)
Rank : 3
Schlafli Type : {159,4}
Number of vertices, edges, etc : 159, 318, 4
Order of s₀s₁s₂ : 159
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) :
   53-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  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);;
s1 := (  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);;
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);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := 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);
s1 := 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);
s2 := Sym(212)!(  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);
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, 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 >;

References : None.
to this polytope