Part of the Atlas of Small Regular Polytopes

Polytope of Type {14,7}

Atlas Canonical Name {14,7}*1792a

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Overview

Group
SmallGroup(1792,1083551)
Rank
3
Schläfli Type
{14,7}
Vertices, edges, …
128, 448, 64
Order of s0s1s2
8
Order of s0s1s2s1
7
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

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)^2)^2> of order 2

32 facets

64 vertex figures

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

32 facets

64 vertex figures

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

16 facets

32 vertex figures

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

16 facets

32 vertex figures

P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, (s0*s1)^2*s2*s1*s0*(s1*s2)^2*s1*s0*s1, (s0*s1)^2*s2*s1*s0*s2*(s1*s0)^2*s1*s2> of order 8

8 facets

16 vertex figures

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

References

None.

to this polytope.

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