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

Overview

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

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{4,4,26}*832

4-fold

8-fold

13-fold

{4,4,2}*128

16-fold

{2,2,13}*104

26-fold

{4,4,2}*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=<(s1*s2)^2> of order 2

26 facets

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

6 vertex figures

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

P/N, where N=<(s0*s1)^2> of order 2

26 facets

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

4 vertex figures

4 of {4,26}*208

Representations

Permutation Representation (GAP)

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

References

None.

to this polytope.