Polytope of Type {2,106,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,106,4}*1696
if this polytope has a name.
Group : SmallGroup(1696,182)
Rank : 4
Schlafli Type : {2,106,4}
Number of vertices, edges, etc : 2, 106, 212, 4
Order of s₀s₁s₂s₃ : 212
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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) :
   2-fold quotients : {2,106,2}*848
   4-fold quotients : {2,53,2}*424
   53-fold quotients : {2,2,4}*32
   106-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 55)(  5, 54)(  6, 53)(  7, 52)(  8, 51)(  9, 50)( 10, 49)( 11, 48)
( 12, 47)( 13, 46)( 14, 45)( 15, 44)( 16, 43)( 17, 42)( 18, 41)( 19, 40)
( 20, 39)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 29, 30)( 57,108)( 58,107)( 59,106)( 60,105)( 61,104)( 62,103)
( 63,102)( 64,101)( 65,100)( 66, 99)( 67, 98)( 68, 97)( 69, 96)( 70, 95)
( 71, 94)( 72, 93)( 73, 92)( 74, 91)( 75, 90)( 76, 89)( 77, 88)( 78, 87)
( 79, 86)( 80, 85)( 81, 84)( 82, 83)(110,161)(111,160)(112,159)(113,158)
(114,157)(115,156)(116,155)(117,154)(118,153)(119,152)(120,151)(121,150)
(122,149)(123,148)(124,147)(125,146)(126,145)(127,144)(128,143)(129,142)
(130,141)(131,140)(132,139)(133,138)(134,137)(135,136)(163,214)(164,213)
(165,212)(166,211)(167,210)(168,209)(169,208)(170,207)(171,206)(172,205)
(173,204)(174,203)(175,202)(176,201)(177,200)(178,199)(179,198)(180,197)
(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)(187,190)(188,189);;
s2 := (  3,  4)(  5, 55)(  6, 54)(  7, 53)(  8, 52)(  9, 51)( 10, 50)( 11, 49)
( 12, 48)( 13, 47)( 14, 46)( 15, 45)( 16, 44)( 17, 43)( 18, 42)( 19, 41)
( 20, 40)( 21, 39)( 22, 38)( 23, 37)( 24, 36)( 25, 35)( 26, 34)( 27, 33)
( 28, 32)( 29, 31)( 56, 57)( 58,108)( 59,107)( 60,106)( 61,105)( 62,104)
( 63,103)( 64,102)( 65,101)( 66,100)( 67, 99)( 68, 98)( 69, 97)( 70, 96)
( 71, 95)( 72, 94)( 73, 93)( 74, 92)( 75, 91)( 76, 90)( 77, 89)( 78, 88)
( 79, 87)( 80, 86)( 81, 85)( 82, 84)(109,163)(110,162)(111,214)(112,213)
(113,212)(114,211)(115,210)(116,209)(117,208)(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)(139,186)(140,185)(141,184)(142,183)(143,182)(144,181)
(145,180)(146,179)(147,178)(148,177)(149,176)(150,175)(151,174)(152,173)
(153,172)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)
(161,164);;
s3 := (  3,109)(  4,110)(  5,111)(  6,112)(  7,113)(  8,114)(  9,115)( 10,116)
( 11,117)( 12,118)( 13,119)( 14,120)( 15,121)( 16,122)( 17,123)( 18,124)
( 19,125)( 20,126)( 21,127)( 22,128)( 23,129)( 24,130)( 25,131)( 26,132)
( 27,133)( 28,134)( 29,135)( 30,136)( 31,137)( 32,138)( 33,139)( 34,140)
( 35,141)( 36,142)( 37,143)( 38,144)( 39,145)( 40,146)( 41,147)( 42,148)
( 43,149)( 44,150)( 45,151)( 46,152)( 47,153)( 48,154)( 49,155)( 50,156)
( 51,157)( 52,158)( 53,159)( 54,160)( 55,161)( 56,162)( 57,163)( 58,164)
( 59,165)( 60,166)( 61,167)( 62,168)( 63,169)( 64,170)( 65,171)( 66,172)
( 67,173)( 68,174)( 69,175)( 70,176)( 71,177)( 72,178)( 73,179)( 74,180)
( 75,181)( 76,182)( 77,183)( 78,184)( 79,185)( 80,186)( 81,187)( 82,188)
( 83,189)( 84,190)( 85,191)( 86,192)( 87,193)( 88,194)( 89,195)( 90,196)
( 91,197)( 92,198)( 93,199)( 94,200)( 95,201)( 96,202)( 97,203)( 98,204)
( 99,205)(100,206)(101,207)(102,208)(103,209)(104,210)(105,211)(106,212)
(107,213)(108,214);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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*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*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(214)!(1,2);
s1 := Sym(214)!(  4, 55)(  5, 54)(  6, 53)(  7, 52)(  8, 51)(  9, 50)( 10, 49)
( 11, 48)( 12, 47)( 13, 46)( 14, 45)( 15, 44)( 16, 43)( 17, 42)( 18, 41)
( 19, 40)( 20, 39)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)
( 27, 32)( 28, 31)( 29, 30)( 57,108)( 58,107)( 59,106)( 60,105)( 61,104)
( 62,103)( 63,102)( 64,101)( 65,100)( 66, 99)( 67, 98)( 68, 97)( 69, 96)
( 70, 95)( 71, 94)( 72, 93)( 73, 92)( 74, 91)( 75, 90)( 76, 89)( 77, 88)
( 78, 87)( 79, 86)( 80, 85)( 81, 84)( 82, 83)(110,161)(111,160)(112,159)
(113,158)(114,157)(115,156)(116,155)(117,154)(118,153)(119,152)(120,151)
(121,150)(122,149)(123,148)(124,147)(125,146)(126,145)(127,144)(128,143)
(129,142)(130,141)(131,140)(132,139)(133,138)(134,137)(135,136)(163,214)
(164,213)(165,212)(166,211)(167,210)(168,209)(169,208)(170,207)(171,206)
(172,205)(173,204)(174,203)(175,202)(176,201)(177,200)(178,199)(179,198)
(180,197)(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)(187,190)
(188,189);
s2 := Sym(214)!(  3,  4)(  5, 55)(  6, 54)(  7, 53)(  8, 52)(  9, 51)( 10, 50)
( 11, 49)( 12, 48)( 13, 47)( 14, 46)( 15, 45)( 16, 44)( 17, 43)( 18, 42)
( 19, 41)( 20, 40)( 21, 39)( 22, 38)( 23, 37)( 24, 36)( 25, 35)( 26, 34)
( 27, 33)( 28, 32)( 29, 31)( 56, 57)( 58,108)( 59,107)( 60,106)( 61,105)
( 62,104)( 63,103)( 64,102)( 65,101)( 66,100)( 67, 99)( 68, 98)( 69, 97)
( 70, 96)( 71, 95)( 72, 94)( 73, 93)( 74, 92)( 75, 91)( 76, 90)( 77, 89)
( 78, 88)( 79, 87)( 80, 86)( 81, 85)( 82, 84)(109,163)(110,162)(111,214)
(112,213)(113,212)(114,211)(115,210)(116,209)(117,208)(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)(139,186)(140,185)(141,184)(142,183)(143,182)
(144,181)(145,180)(146,179)(147,178)(148,177)(149,176)(150,175)(151,174)
(152,173)(153,172)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)
(160,165)(161,164);
s3 := Sym(214)!(  3,109)(  4,110)(  5,111)(  6,112)(  7,113)(  8,114)(  9,115)
( 10,116)( 11,117)( 12,118)( 13,119)( 14,120)( 15,121)( 16,122)( 17,123)
( 18,124)( 19,125)( 20,126)( 21,127)( 22,128)( 23,129)( 24,130)( 25,131)
( 26,132)( 27,133)( 28,134)( 29,135)( 30,136)( 31,137)( 32,138)( 33,139)
( 34,140)( 35,141)( 36,142)( 37,143)( 38,144)( 39,145)( 40,146)( 41,147)
( 42,148)( 43,149)( 44,150)( 45,151)( 46,152)( 47,153)( 48,154)( 49,155)
( 50,156)( 51,157)( 52,158)( 53,159)( 54,160)( 55,161)( 56,162)( 57,163)
( 58,164)( 59,165)( 60,166)( 61,167)( 62,168)( 63,169)( 64,170)( 65,171)
( 66,172)( 67,173)( 68,174)( 69,175)( 70,176)( 71,177)( 72,178)( 73,179)
( 74,180)( 75,181)( 76,182)( 77,183)( 78,184)( 79,185)( 80,186)( 81,187)
( 82,188)( 83,189)( 84,190)( 85,191)( 86,192)( 87,193)( 88,194)( 89,195)
( 90,196)( 91,197)( 92,198)( 93,199)( 94,200)( 95,201)( 96,202)( 97,203)
( 98,204)( 99,205)(100,206)(101,207)(102,208)(103,209)(104,210)(105,211)
(106,212)(107,213)(108,214);
poly := sub<Sym(214)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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*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*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 >;

to this polytope