Polytope of Type {4,55} with group SmallGroup(1760,1271)

Overview

Group: SmallGroup(1760,1271)
Rank: 3
Schläfli Type: {4,55}
Vertices, edges, …: 16, 440, 220
Order of s₀s₁s₂: 55
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

11-fold

{4,5}*160

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=<s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 2

132 facets

88 of {4}*8
44 of {2}*4

8 vertex figures

8 of {55}*110

P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 2

110 facets

110 of {4}*8

8 vertex figures

8 of {55}*110

P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4

66 facets

44 of {4}*8
22 of {2}*4

4 vertex figures

4 of {55}*110

P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4

77 facets

33 of {4}*8
44 of {2}*4

4 vertex figures

4 of {55}*110

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.