Polytope of Type {26,16,2}

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

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

Permutation Representation (Magma) :

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

to this polytope