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

Overview

Group: SmallGroup(1792,1083551)
Rank: 3
Schläfli Type: {4,14}
Vertices, edges, …: 64, 448, 224
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

Quotients maximal quotients in bold

2-fold

{4,7}*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=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 2

112 facets

112 of {4}*8

32 vertex figures

32 of {14}*28

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

112 facets

112 of {4}*8

32 vertex figures

32 of {14}*28

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

56 facets

56 of {4}*8

16 vertex figures

16 of {14}*28

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

56 facets

56 of {4}*8

16 vertex figures

16 of {14}*28

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

28 facets

28 of {4}*8

8 vertex figures

8 of {14}*28

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.