Polytope of Type {6,44}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope