Polytope of Type {52,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {52,8}*1664b
if this polytope has a name.
Group : SmallGroup(1664,6496)
Rank : 3
Schlafli Type : {52,8}
Number of vertices, edges, etc : 104, 416, 16
Order of s₀s₁s₂ : 52
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {52,4}*832
   4-fold quotients : {52,4}*416
   8-fold quotients : {52,2}*208, {26,4}*208
   13-fold quotients : {4,8}*128b
   16-fold quotients : {26,2}*104
   26-fold quotients : {4,4}*64
   32-fold quotients : {13,2}*52
   52-fold quotients : {4,4}*32
   104-fold quotients : {2,4}*16, {4,2}*16
   208-fold quotients : {2,2}*8
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)
( 53, 92)( 54,104)( 55,103)( 56,102)( 57,101)( 58,100)( 59, 99)( 60, 98)
( 61, 97)( 62, 96)( 63, 95)( 64, 94)( 65, 93)( 66, 79)( 67, 91)( 68, 90)
( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)( 74, 84)( 75, 83)( 76, 82)
( 77, 81)( 78, 80)(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)(157,196)(158,208)(159,207)(160,206)(161,205)(162,204)
(163,203)(164,202)(165,201)(166,200)(167,199)(168,198)(169,197)(170,183)
(171,195)(172,194)(173,193)(174,192)(175,191)(176,190)(177,189)(178,188)
(179,187)(180,186)(181,185)(182,184);;
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, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 67)
( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 93)( 80, 92)( 81,104)
( 82,103)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)( 89, 96)
( 90, 95)( 91, 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)( 27,131)( 28,132)( 29,133)( 30,134)( 31,135)( 32,136)
( 33,137)( 34,138)( 35,139)( 36,140)( 37,141)( 38,142)( 39,143)( 40,144)
( 41,145)( 42,146)( 43,147)( 44,148)( 45,149)( 46,150)( 47,151)( 48,152)
( 49,153)( 50,154)( 51,155)( 52,156)( 53,196)( 54,197)( 55,198)( 56,199)
( 57,200)( 58,201)( 59,202)( 60,203)( 61,204)( 62,205)( 63,206)( 64,207)
( 65,208)( 66,183)( 67,184)( 68,185)( 69,186)( 70,187)( 71,188)( 72,189)
( 73,190)( 74,191)( 75,192)( 76,193)( 77,194)( 78,195)( 79,170)( 80,171)
( 81,172)( 82,173)( 83,174)( 84,175)( 85,176)( 86,177)( 87,178)( 88,179)
( 89,180)( 90,181)( 91,182)( 92,157)( 93,158)( 94,159)( 95,160)( 96,161)
( 97,162)( 98,163)( 99,164)(100,165)(101,166)(102,167)(103,168)(104,169);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(208)!(  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)( 53, 92)( 54,104)( 55,103)( 56,102)( 57,101)( 58,100)( 59, 99)
( 60, 98)( 61, 97)( 62, 96)( 63, 95)( 64, 94)( 65, 93)( 66, 79)( 67, 91)
( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)( 74, 84)( 75, 83)
( 76, 82)( 77, 81)( 78, 80)(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)(157,196)(158,208)(159,207)(160,206)(161,205)
(162,204)(163,203)(164,202)(165,201)(166,200)(167,199)(168,198)(169,197)
(170,183)(171,195)(172,194)(173,193)(174,192)(175,191)(176,190)(177,189)
(178,188)(179,187)(180,186)(181,185)(182,184);
s1 := Sym(208)!(  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, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)
( 66, 67)( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 93)( 80, 92)
( 81,104)( 82,103)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)
( 89, 96)( 90, 95)( 91, 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(208)!(  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)( 27,131)( 28,132)( 29,133)( 30,134)( 31,135)
( 32,136)( 33,137)( 34,138)( 35,139)( 36,140)( 37,141)( 38,142)( 39,143)
( 40,144)( 41,145)( 42,146)( 43,147)( 44,148)( 45,149)( 46,150)( 47,151)
( 48,152)( 49,153)( 50,154)( 51,155)( 52,156)( 53,196)( 54,197)( 55,198)
( 56,199)( 57,200)( 58,201)( 59,202)( 60,203)( 61,204)( 62,205)( 63,206)
( 64,207)( 65,208)( 66,183)( 67,184)( 68,185)( 69,186)( 70,187)( 71,188)
( 72,189)( 73,190)( 74,191)( 75,192)( 76,193)( 77,194)( 78,195)( 79,170)
( 80,171)( 81,172)( 82,173)( 83,174)( 84,175)( 85,176)( 86,177)( 87,178)
( 88,179)( 89,180)( 90,181)( 91,182)( 92,157)( 93,158)( 94,159)( 95,160)
( 96,161)( 97,162)( 98,163)( 99,164)(100,165)(101,166)(102,167)(103,168)
(104,169);
poly := sub<Sym(208)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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