Polytope of Type {46,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {46,6,3}*1656
if this polytope has a name.
Group : SmallGroup(1656,116)
Rank : 4
Schlafli Type : {46,6,3}
Number of vertices, edges, etc : 46, 138, 9, 3
Order of s₀s₁s₂s₃ : 138
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   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) :
   3-fold quotients : {46,2,3}*552
   6-fold quotients : {23,2,3}*276
   23-fold quotients : {2,6,3}*72
   69-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)
( 10, 15)( 11, 14)( 12, 13)( 25, 46)( 26, 45)( 27, 44)( 28, 43)( 29, 42)
( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 48, 69)( 49, 68)
( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)( 57, 60)
( 58, 59)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)
( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 94,115)( 95,114)( 96,113)( 97,112)
( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)(117,138)
(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)(125,130)
(126,129)(127,128)(140,161)(141,160)(142,159)(143,158)(144,157)(145,156)
(146,155)(147,154)(148,153)(149,152)(150,151)(163,184)(164,183)(165,182)
(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)(173,174)
(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)
(194,199)(195,198)(196,197);;
s1 := (  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)
( 10, 16)( 11, 15)( 12, 14)( 24, 25)( 26, 46)( 27, 45)( 28, 44)( 29, 43)
( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 48)( 49, 69)
( 50, 68)( 51, 67)( 52, 66)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)
( 58, 60)( 70,140)( 71,139)( 72,161)( 73,160)( 74,159)( 75,158)( 76,157)
( 77,156)( 78,155)( 79,154)( 80,153)( 81,152)( 82,151)( 83,150)( 84,149)
( 85,148)( 86,147)( 87,146)( 88,145)( 89,144)( 90,143)( 91,142)( 92,141)
( 93,163)( 94,162)( 95,184)( 96,183)( 97,182)( 98,181)( 99,180)(100,179)
(101,178)(102,177)(103,176)(104,175)(105,174)(106,173)(107,172)(108,171)
(109,170)(110,169)(111,168)(112,167)(113,166)(114,165)(115,164)(116,186)
(117,185)(118,207)(119,206)(120,205)(121,204)(122,203)(123,202)(124,201)
(125,200)(126,199)(127,198)(128,197)(129,196)(130,195)(131,194)(132,193)
(133,192)(134,191)(135,190)(136,189)(137,188)(138,187);;
s2 := (  1, 70)(  2, 71)(  3, 72)(  4, 73)(  5, 74)(  6, 75)(  7, 76)(  8, 77)
(  9, 78)( 10, 79)( 11, 80)( 12, 81)( 13, 82)( 14, 83)( 15, 84)( 16, 85)
( 17, 86)( 18, 87)( 19, 88)( 20, 89)( 21, 90)( 22, 91)( 23, 92)( 24,116)
( 25,117)( 26,118)( 27,119)( 28,120)( 29,121)( 30,122)( 31,123)( 32,124)
( 33,125)( 34,126)( 35,127)( 36,128)( 37,129)( 38,130)( 39,131)( 40,132)
( 41,133)( 42,134)( 43,135)( 44,136)( 45,137)( 46,138)( 47, 93)( 48, 94)
( 49, 95)( 50, 96)( 51, 97)( 52, 98)( 53, 99)( 54,100)( 55,101)( 56,102)
( 57,103)( 58,104)( 59,105)( 60,106)( 61,107)( 62,108)( 63,109)( 64,110)
( 65,111)( 66,112)( 67,113)( 68,114)( 69,115)(162,185)(163,186)(164,187)
(165,188)(166,189)(167,190)(168,191)(169,192)(170,193)(171,194)(172,195)
(173,196)(174,197)(175,198)(176,199)(177,200)(178,201)(179,202)(180,203)
(181,204)(182,205)(183,206)(184,207);;
s3 := (  1, 24)(  2, 25)(  3, 26)(  4, 27)(  5, 28)(  6, 29)(  7, 30)(  8, 31)
(  9, 32)( 10, 33)( 11, 34)( 12, 35)( 13, 36)( 14, 37)( 15, 38)( 16, 39)
( 17, 40)( 18, 41)( 19, 42)( 20, 43)( 21, 44)( 22, 45)( 23, 46)( 70,162)
( 71,163)( 72,164)( 73,165)( 74,166)( 75,167)( 76,168)( 77,169)( 78,170)
( 79,171)( 80,172)( 81,173)( 82,174)( 83,175)( 84,176)( 85,177)( 86,178)
( 87,179)( 88,180)( 89,181)( 90,182)( 91,183)( 92,184)( 93,139)( 94,140)
( 95,141)( 96,142)( 97,143)( 98,144)( 99,145)(100,146)(101,147)(102,148)
(103,149)(104,150)(105,151)(106,152)(107,153)(108,154)(109,155)(110,156)
(111,157)(112,158)(113,159)(114,160)(115,161)(116,185)(117,186)(118,187)
(119,188)(120,189)(121,190)(122,191)(123,192)(124,193)(125,194)(126,195)
(127,196)(128,197)(129,198)(130,199)(131,200)(132,201)(133,202)(134,203)
(135,204)(136,205)(137,206)(138,207);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(207)!(  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)
(  9, 16)( 10, 15)( 11, 14)( 12, 13)( 25, 46)( 26, 45)( 27, 44)( 28, 43)
( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 48, 69)
( 49, 68)( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)
( 57, 60)( 58, 59)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)
( 77, 86)( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 94,115)( 95,114)( 96,113)
( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)
(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)
(125,130)(126,129)(127,128)(140,161)(141,160)(142,159)(143,158)(144,157)
(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)(163,184)(164,183)
(165,182)(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)
(173,174)(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)
(193,200)(194,199)(195,198)(196,197);
s1 := Sym(207)!(  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)
(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 24, 25)( 26, 46)( 27, 45)( 28, 44)
( 29, 43)( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 48)
( 49, 69)( 50, 68)( 51, 67)( 52, 66)( 53, 65)( 54, 64)( 55, 63)( 56, 62)
( 57, 61)( 58, 60)( 70,140)( 71,139)( 72,161)( 73,160)( 74,159)( 75,158)
( 76,157)( 77,156)( 78,155)( 79,154)( 80,153)( 81,152)( 82,151)( 83,150)
( 84,149)( 85,148)( 86,147)( 87,146)( 88,145)( 89,144)( 90,143)( 91,142)
( 92,141)( 93,163)( 94,162)( 95,184)( 96,183)( 97,182)( 98,181)( 99,180)
(100,179)(101,178)(102,177)(103,176)(104,175)(105,174)(106,173)(107,172)
(108,171)(109,170)(110,169)(111,168)(112,167)(113,166)(114,165)(115,164)
(116,186)(117,185)(118,207)(119,206)(120,205)(121,204)(122,203)(123,202)
(124,201)(125,200)(126,199)(127,198)(128,197)(129,196)(130,195)(131,194)
(132,193)(133,192)(134,191)(135,190)(136,189)(137,188)(138,187);
s2 := Sym(207)!(  1, 70)(  2, 71)(  3, 72)(  4, 73)(  5, 74)(  6, 75)(  7, 76)
(  8, 77)(  9, 78)( 10, 79)( 11, 80)( 12, 81)( 13, 82)( 14, 83)( 15, 84)
( 16, 85)( 17, 86)( 18, 87)( 19, 88)( 20, 89)( 21, 90)( 22, 91)( 23, 92)
( 24,116)( 25,117)( 26,118)( 27,119)( 28,120)( 29,121)( 30,122)( 31,123)
( 32,124)( 33,125)( 34,126)( 35,127)( 36,128)( 37,129)( 38,130)( 39,131)
( 40,132)( 41,133)( 42,134)( 43,135)( 44,136)( 45,137)( 46,138)( 47, 93)
( 48, 94)( 49, 95)( 50, 96)( 51, 97)( 52, 98)( 53, 99)( 54,100)( 55,101)
( 56,102)( 57,103)( 58,104)( 59,105)( 60,106)( 61,107)( 62,108)( 63,109)
( 64,110)( 65,111)( 66,112)( 67,113)( 68,114)( 69,115)(162,185)(163,186)
(164,187)(165,188)(166,189)(167,190)(168,191)(169,192)(170,193)(171,194)
(172,195)(173,196)(174,197)(175,198)(176,199)(177,200)(178,201)(179,202)
(180,203)(181,204)(182,205)(183,206)(184,207);
s3 := Sym(207)!(  1, 24)(  2, 25)(  3, 26)(  4, 27)(  5, 28)(  6, 29)(  7, 30)
(  8, 31)(  9, 32)( 10, 33)( 11, 34)( 12, 35)( 13, 36)( 14, 37)( 15, 38)
( 16, 39)( 17, 40)( 18, 41)( 19, 42)( 20, 43)( 21, 44)( 22, 45)( 23, 46)
( 70,162)( 71,163)( 72,164)( 73,165)( 74,166)( 75,167)( 76,168)( 77,169)
( 78,170)( 79,171)( 80,172)( 81,173)( 82,174)( 83,175)( 84,176)( 85,177)
( 86,178)( 87,179)( 88,180)( 89,181)( 90,182)( 91,183)( 92,184)( 93,139)
( 94,140)( 95,141)( 96,142)( 97,143)( 98,144)( 99,145)(100,146)(101,147)
(102,148)(103,149)(104,150)(105,151)(106,152)(107,153)(108,154)(109,155)
(110,156)(111,157)(112,158)(113,159)(114,160)(115,161)(116,185)(117,186)
(118,187)(119,188)(120,189)(121,190)(122,191)(123,192)(124,193)(125,194)
(126,195)(127,196)(128,197)(129,198)(130,199)(131,200)(132,201)(133,202)
(134,203)(135,204)(136,205)(137,206)(138,207);
poly := sub<Sym(207)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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