Polytope of Type {26,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,4,4}*1664
Also Known As : {{26,4|2},{4,4}4}. if this polytope has another name.
Group : SmallGroup(1664,13892)
Rank : 4
Schlafli Type : {26,4,4}
Number of vertices, edges, etc : 26, 104, 16, 8
Order of s0s1s2s3 : 52
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {26,4,4}*832
4-fold quotients : {26,2,4}*416, {26,4,2}*416
8-fold quotients : {13,2,4}*208, {26,2,2}*208
13-fold quotients : {2,4,4}*128
16-fold quotients : {13,2,2}*104
26-fold quotients : {2,4,4}*64
52-fold quotients : {2,2,4}*32, {2,4,2}*32
104-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 53)( 2, 65)( 3, 64)( 4, 63)( 5, 62)( 6, 61)( 7, 60)( 8, 59)
( 9, 58)( 10, 57)( 11, 56)( 12, 55)( 13, 54)( 14, 66)( 15, 78)( 16, 77)
( 17, 76)( 18, 75)( 19, 74)( 20, 73)( 21, 72)( 22, 71)( 23, 70)( 24, 69)
( 25, 68)( 26, 67)( 27, 79)( 28, 91)( 29, 90)( 30, 89)( 31, 88)( 32, 87)
( 33, 86)( 34, 85)( 35, 84)( 36, 83)( 37, 82)( 38, 81)( 39, 80)( 40, 92)
( 41,104)( 42,103)( 43,102)( 44,101)( 45,100)( 46, 99)( 47, 98)( 48, 97)
( 49, 96)( 50, 95)( 51, 94)( 52, 93)(105,157)(106,169)(107,168)(108,167)
(109,166)(110,165)(111,164)(112,163)(113,162)(114,161)(115,160)(116,159)
(117,158)(118,170)(119,182)(120,181)(121,180)(122,179)(123,178)(124,177)
(125,176)(126,175)(127,174)(128,173)(129,172)(130,171)(131,183)(132,195)
(133,194)(134,193)(135,192)(136,191)(137,190)(138,189)(139,188)(140,187)
(141,186)(142,185)(143,184)(144,196)(145,208)(146,207)(147,206)(148,205)
(149,204)(150,203)(151,202)(152,201)(153,200)(154,199)(155,198)(156,197);;
s1 := ( 1, 54)( 2, 53)( 3, 65)( 4, 64)( 5, 63)( 6, 62)( 7, 61)( 8, 60)
( 9, 59)( 10, 58)( 11, 57)( 12, 56)( 13, 55)( 14, 67)( 15, 66)( 16, 78)
( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 72)( 23, 71)( 24, 70)
( 25, 69)( 26, 68)( 27, 93)( 28, 92)( 29,104)( 30,103)( 31,102)( 32,101)
( 33,100)( 34, 99)( 35, 98)( 36, 97)( 37, 96)( 38, 95)( 39, 94)( 40, 80)
( 41, 79)( 42, 91)( 43, 90)( 44, 89)( 45, 88)( 46, 87)( 47, 86)( 48, 85)
( 49, 84)( 50, 83)( 51, 82)( 52, 81)(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 := (105,131)(106,132)(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)(157,183)(158,184)(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);;
s3 := ( 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)( 53,157)( 54,158)( 55,159)( 56,160)
( 57,161)( 58,162)( 59,163)( 60,164)( 61,165)( 62,166)( 63,167)( 64,168)
( 65,169)( 66,170)( 67,171)( 68,172)( 69,173)( 70,174)( 71,175)( 72,176)
( 73,177)( 74,178)( 75,179)( 76,180)( 77,181)( 78,182)( 79,183)( 80,184)
( 81,185)( 82,186)( 83,187)( 84,188)( 85,189)( 86,190)( 87,191)( 88,192)
( 89,193)( 90,194)( 91,195)( 92,196)( 93,197)( 94,198)( 95,199)( 96,200)
( 97,201)( 98,202)( 99,203)(100,204)(101,205)(102,206)(103,207)(104,208);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*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(208)!( 1, 53)( 2, 65)( 3, 64)( 4, 63)( 5, 62)( 6, 61)( 7, 60)
( 8, 59)( 9, 58)( 10, 57)( 11, 56)( 12, 55)( 13, 54)( 14, 66)( 15, 78)
( 16, 77)( 17, 76)( 18, 75)( 19, 74)( 20, 73)( 21, 72)( 22, 71)( 23, 70)
( 24, 69)( 25, 68)( 26, 67)( 27, 79)( 28, 91)( 29, 90)( 30, 89)( 31, 88)
( 32, 87)( 33, 86)( 34, 85)( 35, 84)( 36, 83)( 37, 82)( 38, 81)( 39, 80)
( 40, 92)( 41,104)( 42,103)( 43,102)( 44,101)( 45,100)( 46, 99)( 47, 98)
( 48, 97)( 49, 96)( 50, 95)( 51, 94)( 52, 93)(105,157)(106,169)(107,168)
(108,167)(109,166)(110,165)(111,164)(112,163)(113,162)(114,161)(115,160)
(116,159)(117,158)(118,170)(119,182)(120,181)(121,180)(122,179)(123,178)
(124,177)(125,176)(126,175)(127,174)(128,173)(129,172)(130,171)(131,183)
(132,195)(133,194)(134,193)(135,192)(136,191)(137,190)(138,189)(139,188)
(140,187)(141,186)(142,185)(143,184)(144,196)(145,208)(146,207)(147,206)
(148,205)(149,204)(150,203)(151,202)(152,201)(153,200)(154,199)(155,198)
(156,197);
s1 := Sym(208)!( 1, 54)( 2, 53)( 3, 65)( 4, 64)( 5, 63)( 6, 62)( 7, 61)
( 8, 60)( 9, 59)( 10, 58)( 11, 57)( 12, 56)( 13, 55)( 14, 67)( 15, 66)
( 16, 78)( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 72)( 23, 71)
( 24, 70)( 25, 69)( 26, 68)( 27, 93)( 28, 92)( 29,104)( 30,103)( 31,102)
( 32,101)( 33,100)( 34, 99)( 35, 98)( 36, 97)( 37, 96)( 38, 95)( 39, 94)
( 40, 80)( 41, 79)( 42, 91)( 43, 90)( 44, 89)( 45, 88)( 46, 87)( 47, 86)
( 48, 85)( 49, 84)( 50, 83)( 51, 82)( 52, 81)(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)!(105,131)(106,132)(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)(157,183)(158,184)(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);
s3 := 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)( 53,157)( 54,158)( 55,159)
( 56,160)( 57,161)( 58,162)( 59,163)( 60,164)( 61,165)( 62,166)( 63,167)
( 64,168)( 65,169)( 66,170)( 67,171)( 68,172)( 69,173)( 70,174)( 71,175)
( 72,176)( 73,177)( 74,178)( 75,179)( 76,180)( 77,181)( 78,182)( 79,183)
( 80,184)( 81,185)( 82,186)( 83,187)( 84,188)( 85,189)( 86,190)( 87,191)
( 88,192)( 89,193)( 90,194)( 91,195)( 92,196)( 93,197)( 94,198)( 95,199)
( 96,200)( 97,201)( 98,202)( 99,203)(100,204)(101,205)(102,206)(103,207)
(104,208);
poly := sub<Sym(208)|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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*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 >;
References : None.
to this polytope