Polytope of Type {2,4,26,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,26,4}*1664
if this polytope has a name.
Group : SmallGroup(1664,17946)
Rank : 5
Schlafli Type : {2,4,26,4}
Number of vertices, edges, etc : 2, 4, 52, 52, 4
Order of s0s1s2s3s4 : 52
Order of s0s1s2s3s4s3s2s1 : 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 : {2,2,26,4}*832, {2,4,26,2}*832
4-fold quotients : {2,2,26,2}*416
8-fold quotients : {2,2,13,2}*208
13-fold quotients : {2,4,2,4}*128
26-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
52-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (107,133)(108,134)(109,135)(110,136)(111,137)(112,138)(113,139)(114,140)
(115,141)(116,142)(117,143)(118,144)(119,145)(120,146)(121,147)(122,148)
(123,149)(124,150)(125,151)(126,152)(127,153)(128,154)(129,155)(130,156)
(131,157)(132,158)(159,185)(160,186)(161,187)(162,188)(163,189)(164,190)
(165,191)(166,192)(167,193)(168,194)(169,195)(170,196)(171,197)(172,198)
(173,199)(174,200)(175,201)(176,202)(177,203)(178,204)(179,205)(180,206)
(181,207)(182,208)(183,209)(184,210);;
s2 := ( 3,107)( 4,119)( 5,118)( 6,117)( 7,116)( 8,115)( 9,114)( 10,113)
( 11,112)( 12,111)( 13,110)( 14,109)( 15,108)( 16,120)( 17,132)( 18,131)
( 19,130)( 20,129)( 21,128)( 22,127)( 23,126)( 24,125)( 25,124)( 26,123)
( 27,122)( 28,121)( 29,133)( 30,145)( 31,144)( 32,143)( 33,142)( 34,141)
( 35,140)( 36,139)( 37,138)( 38,137)( 39,136)( 40,135)( 41,134)( 42,146)
( 43,158)( 44,157)( 45,156)( 46,155)( 47,154)( 48,153)( 49,152)( 50,151)
( 51,150)( 52,149)( 53,148)( 54,147)( 55,185)( 56,197)( 57,196)( 58,195)
( 59,194)( 60,193)( 61,192)( 62,191)( 63,190)( 64,189)( 65,188)( 66,187)
( 67,186)( 68,198)( 69,210)( 70,209)( 71,208)( 72,207)( 73,206)( 74,205)
( 75,204)( 76,203)( 77,202)( 78,201)( 79,200)( 80,199)( 81,159)( 82,171)
( 83,170)( 84,169)( 85,168)( 86,167)( 87,166)( 88,165)( 89,164)( 90,163)
( 91,162)( 92,161)( 93,160)( 94,172)( 95,184)( 96,183)( 97,182)( 98,181)
( 99,180)(100,179)(101,178)(102,177)(103,176)(104,175)(105,174)(106,173);;
s3 := ( 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, 30)( 31, 41)( 32, 40)( 33, 39)
( 34, 38)( 35, 37)( 42, 43)( 44, 54)( 45, 53)( 46, 52)( 47, 51)( 48, 50)
( 55, 95)( 56, 94)( 57,106)( 58,105)( 59,104)( 60,103)( 61,102)( 62,101)
( 63,100)( 64, 99)( 65, 98)( 66, 97)( 67, 96)( 68, 82)( 69, 81)( 70, 93)
( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 78, 85)
( 79, 84)( 80, 83)(107,108)(109,119)(110,118)(111,117)(112,116)(113,115)
(120,121)(122,132)(123,131)(124,130)(125,129)(126,128)(133,134)(135,145)
(136,144)(137,143)(138,142)(139,141)(146,147)(148,158)(149,157)(150,156)
(151,155)(152,154)(159,199)(160,198)(161,210)(162,209)(163,208)(164,207)
(165,206)(166,205)(167,204)(168,203)(169,202)(170,201)(171,200)(172,186)
(173,185)(174,197)(175,196)(176,195)(177,194)(178,193)(179,192)(180,191)
(181,190)(182,189)(183,188)(184,187);;
s4 := ( 3, 55)( 4, 56)( 5, 57)( 6, 58)( 7, 59)( 8, 60)( 9, 61)( 10, 62)
( 11, 63)( 12, 64)( 13, 65)( 14, 66)( 15, 67)( 16, 68)( 17, 69)( 18, 70)
( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 75)( 24, 76)( 25, 77)( 26, 78)
( 27, 79)( 28, 80)( 29, 81)( 30, 82)( 31, 83)( 32, 84)( 33, 85)( 34, 86)
( 35, 87)( 36, 88)( 37, 89)( 38, 90)( 39, 91)( 40, 92)( 41, 93)( 42, 94)
( 43, 95)( 44, 96)( 45, 97)( 46, 98)( 47, 99)( 48,100)( 49,101)( 50,102)
( 51,103)( 52,104)( 53,105)( 54,106)(107,185)(108,186)(109,187)(110,188)
(111,189)(112,190)(113,191)(114,192)(115,193)(116,194)(117,195)(118,196)
(119,197)(120,198)(121,199)(122,200)(123,201)(124,202)(125,203)(126,204)
(127,205)(128,206)(129,207)(130,208)(131,209)(132,210)(133,159)(134,160)
(135,161)(136,162)(137,163)(138,164)(139,165)(140,166)(141,167)(142,168)
(143,169)(144,170)(145,171)(146,172)(147,173)(148,174)(149,175)(150,176)
(151,177)(152,178)(153,179)(154,180)(155,181)(156,182)(157,183)(158,184);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(210)!(1,2);
s1 := Sym(210)!(107,133)(108,134)(109,135)(110,136)(111,137)(112,138)(113,139)
(114,140)(115,141)(116,142)(117,143)(118,144)(119,145)(120,146)(121,147)
(122,148)(123,149)(124,150)(125,151)(126,152)(127,153)(128,154)(129,155)
(130,156)(131,157)(132,158)(159,185)(160,186)(161,187)(162,188)(163,189)
(164,190)(165,191)(166,192)(167,193)(168,194)(169,195)(170,196)(171,197)
(172,198)(173,199)(174,200)(175,201)(176,202)(177,203)(178,204)(179,205)
(180,206)(181,207)(182,208)(183,209)(184,210);
s2 := Sym(210)!( 3,107)( 4,119)( 5,118)( 6,117)( 7,116)( 8,115)( 9,114)
( 10,113)( 11,112)( 12,111)( 13,110)( 14,109)( 15,108)( 16,120)( 17,132)
( 18,131)( 19,130)( 20,129)( 21,128)( 22,127)( 23,126)( 24,125)( 25,124)
( 26,123)( 27,122)( 28,121)( 29,133)( 30,145)( 31,144)( 32,143)( 33,142)
( 34,141)( 35,140)( 36,139)( 37,138)( 38,137)( 39,136)( 40,135)( 41,134)
( 42,146)( 43,158)( 44,157)( 45,156)( 46,155)( 47,154)( 48,153)( 49,152)
( 50,151)( 51,150)( 52,149)( 53,148)( 54,147)( 55,185)( 56,197)( 57,196)
( 58,195)( 59,194)( 60,193)( 61,192)( 62,191)( 63,190)( 64,189)( 65,188)
( 66,187)( 67,186)( 68,198)( 69,210)( 70,209)( 71,208)( 72,207)( 73,206)
( 74,205)( 75,204)( 76,203)( 77,202)( 78,201)( 79,200)( 80,199)( 81,159)
( 82,171)( 83,170)( 84,169)( 85,168)( 86,167)( 87,166)( 88,165)( 89,164)
( 90,163)( 91,162)( 92,161)( 93,160)( 94,172)( 95,184)( 96,183)( 97,182)
( 98,181)( 99,180)(100,179)(101,178)(102,177)(103,176)(104,175)(105,174)
(106,173);
s3 := 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, 30)( 31, 41)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 42, 43)( 44, 54)( 45, 53)( 46, 52)( 47, 51)
( 48, 50)( 55, 95)( 56, 94)( 57,106)( 58,105)( 59,104)( 60,103)( 61,102)
( 62,101)( 63,100)( 64, 99)( 65, 98)( 66, 97)( 67, 96)( 68, 82)( 69, 81)
( 70, 93)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)
( 78, 85)( 79, 84)( 80, 83)(107,108)(109,119)(110,118)(111,117)(112,116)
(113,115)(120,121)(122,132)(123,131)(124,130)(125,129)(126,128)(133,134)
(135,145)(136,144)(137,143)(138,142)(139,141)(146,147)(148,158)(149,157)
(150,156)(151,155)(152,154)(159,199)(160,198)(161,210)(162,209)(163,208)
(164,207)(165,206)(166,205)(167,204)(168,203)(169,202)(170,201)(171,200)
(172,186)(173,185)(174,197)(175,196)(176,195)(177,194)(178,193)(179,192)
(180,191)(181,190)(182,189)(183,188)(184,187);
s4 := Sym(210)!( 3, 55)( 4, 56)( 5, 57)( 6, 58)( 7, 59)( 8, 60)( 9, 61)
( 10, 62)( 11, 63)( 12, 64)( 13, 65)( 14, 66)( 15, 67)( 16, 68)( 17, 69)
( 18, 70)( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 75)( 24, 76)( 25, 77)
( 26, 78)( 27, 79)( 28, 80)( 29, 81)( 30, 82)( 31, 83)( 32, 84)( 33, 85)
( 34, 86)( 35, 87)( 36, 88)( 37, 89)( 38, 90)( 39, 91)( 40, 92)( 41, 93)
( 42, 94)( 43, 95)( 44, 96)( 45, 97)( 46, 98)( 47, 99)( 48,100)( 49,101)
( 50,102)( 51,103)( 52,104)( 53,105)( 54,106)(107,185)(108,186)(109,187)
(110,188)(111,189)(112,190)(113,191)(114,192)(115,193)(116,194)(117,195)
(118,196)(119,197)(120,198)(121,199)(122,200)(123,201)(124,202)(125,203)
(126,204)(127,205)(128,206)(129,207)(130,208)(131,209)(132,210)(133,159)
(134,160)(135,161)(136,162)(137,163)(138,164)(139,165)(140,166)(141,167)
(142,168)(143,169)(144,170)(145,171)(146,172)(147,173)(148,174)(149,175)
(150,176)(151,177)(152,178)(153,179)(154,180)(155,181)(156,182)(157,183)
(158,184);
poly := sub<Sym(210)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope