Part of the Atlas of Small Regular Polytopes

Polytope of Type {14,4}

Atlas Canonical Name {14,4}*1792b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1792,1083551)
Rank
3
Schläfli Type
{14,4}
Vertices, edges, …
224, 448, 64
Order of s0s1s2
7
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

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

32 facets

112 vertex figures

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

32 facets

112 vertex figures

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

16 facets

56 vertex figures

P/N, where N=<(s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1*s2, (s0*s1)^2*s2*(s1*s0)^3*s1*s2*s1*s0*s2*s1*s2> of order 4

16 facets

56 vertex figures

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

8 facets

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

References

None.

to this polytope.

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