Polytope of Type {147,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {147,4}*1176
if this polytope has a name.
Group : SmallGroup(1176,45)
Rank : 3
Schlafli Type : {147,4}
Number of vertices, edges, etc : 147, 294, 4
Order of s₀s₁s₂ : 147
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) :
   7-fold quotients : {21,4}*168
   49-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope