Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,7}

Atlas Canonical Name {4,7}*1792a

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Overview

Group
SmallGroup(1792,1083551)
Rank
3
Schläfli Type
{4,7}
Vertices, edges, …
128, 448, 224
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=<(s1*s0*s2)^2*s1*s0*s1*s2*s1*s0*s2*s1> of order 2

120 facets

64 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

64 vertex figures

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

112 facets

64 vertex figures

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

32 vertex figures

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

64 facets

32 vertex figures

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

56 facets

32 vertex figures

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

60 facets

32 vertex figures

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

60 facets

32 vertex figures

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

16 vertex figures

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

References

None.

to this polytope.

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