Polytope of Type {14,4} with group SmallGroup(1792,1083551)

Overview

Group: SmallGroup(1792,1083551)
Rank: 3
Schläfli Type: {14,4}
Vertices, edges, …: 224, 448, 64
Order of s₀s₁s₂: 14
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie

Quotients maximal quotients in bold

2-fold

{7,4}*896

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*s2*(s1*s0)^3*s1*(s2*s1*s0)^2*s1> of order 2

32 facets

32 of {14}*28

112 vertex figures

112 of {4}*8

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

32 facets

32 of {14}*28

112 vertex figures

112 of {4}*8

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

16 facets

16 of {14}*28

56 vertex figures

56 of {4}*8

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

16 facets

16 of {14}*28

56 vertex figures

56 of {4}*8

P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*(s1*s0)^2*s1*s2, s0*s2*s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8

8 facets

8 of {14}*28

28 vertex figures

28 of {4}*8

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.