Polytope of Type {106,4,2}

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

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

to this polytope