Polytope of Type {44,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,6}*1584
if this polytope has a name.
Group : SmallGroup(1584,672)
Rank : 3
Schlafli Type : {44,6}
Number of vertices, edges, etc : 132, 396, 18
Order of s₀s₁s₂ : 44
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {44,6}*792
   9-fold quotients : {44,2}*176
   11-fold quotients : {4,6}*144
   18-fold quotients : {22,2}*88
   22-fold quotients : {4,6}*72
   36-fold quotients : {11,2}*44
   99-fold quotients : {4,2}*16
   198-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope