Polytope of Type {4,40} with group SmallGroup(1280,1116434)

Overview

Group: SmallGroup(1280,1116434)
Rank: 3
Schläfli Type: {4,40}
Vertices, edges, …: 16, 320, 160
Order of s₀s₁s₂: 40
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

2-fold

{4,20}*640c

4-fold

{4,10}*320a

8-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*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2*s1> of order 2

80 facets

80 of {4}*8

8 vertex figures

8 of {40}*80

Representations

Permutation Representation (GAP)

s0 := (  1,108)(  2,107)(  3,105)(  4,106)(  5,112)(  6,111)(  7,109)(  8,110)(  9, 99)( 10,100)( 11, 98)( 12, 97)( 13,103)( 14,104)( 15,102)( 16,101)( 17,124)( 18,123)( 19,121)( 20,122)( 21,128)( 22,127)( 23,125)( 24,126)( 25,115)( 26,116)( 27,114)( 28,113)( 29,119)( 30,120)( 31,118)( 32,117)( 33, 76)( 34, 75)( 35, 73)( 36, 74)( 37, 80)( 38, 79)( 39, 77)( 40, 78)( 41, 67)( 42, 68)( 43, 66)( 44, 65)( 45, 71)( 46, 72)( 47, 70)( 48, 69)( 49, 92)( 50, 91)( 51, 89)( 52, 90)( 53, 96)( 54, 95)( 55, 93)( 56, 94)( 57, 83)( 58, 84)( 59, 82)( 60, 81)( 61, 87)( 62, 88)( 63, 86)( 64, 85);;
s1 := (  3,  4)(  5,  7)(  6,  8)(  9, 65)( 10, 66)( 11, 68)( 12, 67)( 13, 71)( 14, 72)( 15, 69)( 16, 70)( 17, 90)( 18, 89)( 19, 91)( 20, 92)( 21, 96)( 22, 95)( 23, 94)( 24, 93)( 25, 26)( 29, 32)( 30, 31)( 33,114)( 34,113)( 35,115)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)( 41, 50)( 42, 49)( 43, 51)( 44, 52)( 45, 56)( 46, 55)( 47, 54)( 48, 53)( 57,106)( 58,105)( 59,107)( 60,108)( 61,112)( 62,111)( 63,110)( 64,109)( 73, 74)( 77, 80)( 78, 79)( 83, 84)( 85, 87)( 86, 88)( 97,121)( 98,122)( 99,124)(100,123)(101,127)(102,128)(103,125)(104,126);;
s2 := (  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9,101)( 10,102)( 11,104)( 12,103)( 13, 97)( 14, 98)( 15,100)( 16, 99)( 17, 61)( 18, 62)( 19, 64)( 20, 63)( 21, 57)( 22, 58)( 23, 60)( 24, 59)( 25, 94)( 26, 93)( 27, 95)( 28, 96)( 29, 90)( 30, 89)( 31, 91)( 32, 92)( 33, 77)( 34, 78)( 35, 80)( 36, 79)( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 46)( 42, 45)( 43, 47)( 44, 48)( 49,117)( 50,118)( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)( 56,115)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 81,125)( 82,126)( 83,128)( 84,127)( 85,121)( 86,122)( 87,124)( 88,123)(105,110)(106,109)(107,111)(108,112);;
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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(128)!(  1,108)(  2,107)(  3,105)(  4,106)(  5,112)(  6,111)(  7,109)(  8,110)(  9, 99)( 10,100)( 11, 98)( 12, 97)( 13,103)( 14,104)( 15,102)( 16,101)( 17,124)( 18,123)( 19,121)( 20,122)( 21,128)( 22,127)( 23,125)( 24,126)( 25,115)( 26,116)( 27,114)( 28,113)( 29,119)( 30,120)( 31,118)( 32,117)( 33, 76)( 34, 75)( 35, 73)( 36, 74)( 37, 80)( 38, 79)( 39, 77)( 40, 78)( 41, 67)( 42, 68)( 43, 66)( 44, 65)( 45, 71)( 46, 72)( 47, 70)( 48, 69)( 49, 92)( 50, 91)( 51, 89)( 52, 90)( 53, 96)( 54, 95)( 55, 93)( 56, 94)( 57, 83)( 58, 84)( 59, 82)( 60, 81)( 61, 87)( 62, 88)( 63, 86)( 64, 85);
s1 := Sym(128)!(  3,  4)(  5,  7)(  6,  8)(  9, 65)( 10, 66)( 11, 68)( 12, 67)( 13, 71)( 14, 72)( 15, 69)( 16, 70)( 17, 90)( 18, 89)( 19, 91)( 20, 92)( 21, 96)( 22, 95)( 23, 94)( 24, 93)( 25, 26)( 29, 32)( 30, 31)( 33,114)( 34,113)( 35,115)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)( 41, 50)( 42, 49)( 43, 51)( 44, 52)( 45, 56)( 46, 55)( 47, 54)( 48, 53)( 57,106)( 58,105)( 59,107)( 60,108)( 61,112)( 62,111)( 63,110)( 64,109)( 73, 74)( 77, 80)( 78, 79)( 83, 84)( 85, 87)( 86, 88)( 97,121)( 98,122)( 99,124)(100,123)(101,127)(102,128)(103,125)(104,126);
s2 := Sym(128)!(  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9,101)( 10,102)( 11,104)( 12,103)( 13, 97)( 14, 98)( 15,100)( 16, 99)( 17, 61)( 18, 62)( 19, 64)( 20, 63)( 21, 57)( 22, 58)( 23, 60)( 24, 59)( 25, 94)( 26, 93)( 27, 95)( 28, 96)( 29, 90)( 30, 89)( 31, 91)( 32, 92)( 33, 77)( 34, 78)( 35, 80)( 36, 79)( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 46)( 42, 45)( 43, 47)( 44, 48)( 49,117)( 50,118)( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)( 56,115)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 81,125)( 82,126)( 83,128)( 84,127)( 85,121)( 86,122)( 87,124)( 88,123)(105,110)(106,109)(107,111)(108,112);
poly := sub<Sym(128)|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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.