Polytope of Type {2,26,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,26,16}*1664
if this polytope has a name.
Group : SmallGroup(1664,17614)
Rank : 4
Schlafli Type : {2,26,16}
Number of vertices, edges, etc : 2, 26, 208, 16
Order of s₀s₁s₂s₃ : 208
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 : {2,26,8}*832
   4-fold quotients : {2,26,4}*416
   8-fold quotients : {2,26,2}*208
   13-fold quotients : {2,2,16}*128
   16-fold quotients : {2,13,2}*104
   26-fold quotients : {2,2,8}*64
   52-fold quotients : {2,2,4}*32
   104-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope