Polytope of Type {26,4,4} with group SmallGroup(1664,13892)

Overview

Group: SmallGroup(1664,13892)
Rank: 4
Schläfli Type: {26,4,4}
Vertices, edges, …: 26, 104, 16, 8
Order of s₀s₁s₂s₃: 52
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{26,4|2},{4,4}₄}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{26,4,4}*832

4-fold

8-fold

13-fold

{2,4,4}*128

16-fold

{13,2,2}*104

26-fold

{2,4,4}*64

52-fold

104-fold

{2,2,2}*16

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s2*s3)^2> of order 2

4 facets

4 of {26,4}*208

26 vertex figures

26 of 2-fold non-regular quotient of {4,4}*64

P/N, where N=<(s1*s2)^2> of order 2

6 facets

4 of {26,2}*104
2 of {26,4}*208

26 vertex figures

26 of 2-fold non-regular quotient of {4,4}*64

Representations

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.