Part of the Atlas of Small Regular Polytopes

Polytope of Type {111,4}

Atlas Canonical Name {111,4}*888

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(888,48)
Rank
3
Schläfli Type
{111,4}
Vertices, edges, …
111, 222, 4
Order of s0s1s2
111
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable
  • Flat
  • Self-Petrie

Quotients maximal quotients in bold

37-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := (  2,  3)(  5,145)(  6,147)(  7,146)(  8,148)(  9,141)( 10,143)( 11,142)( 12,144)( 13,137)( 14,139)( 15,138)( 16,140)( 17,133)( 18,135)( 19,134)( 20,136)( 21,129)( 22,131)( 23,130)( 24,132)( 25,125)( 26,127)( 27,126)( 28,128)( 29,121)( 30,123)( 31,122)( 32,124)( 33,117)( 34,119)( 35,118)( 36,120)( 37,113)( 38,115)( 39,114)( 40,116)( 41,109)( 42,111)( 43,110)( 44,112)( 45,105)( 46,107)( 47,106)( 48,108)( 49,101)( 50,103)( 51,102)( 52,104)( 53, 97)( 54, 99)( 55, 98)( 56,100)( 57, 93)( 58, 95)( 59, 94)( 60, 96)( 61, 89)( 62, 91)( 63, 90)( 64, 92)( 65, 85)( 66, 87)( 67, 86)( 68, 88)( 69, 81)( 70, 83)( 71, 82)( 72, 84)( 73, 77)( 74, 79)( 75, 78)( 76, 80);;
s1 := (  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9,145)( 10,146)( 11,148)( 12,147)( 13,141)( 14,142)( 15,144)( 16,143)( 17,137)( 18,138)( 19,140)( 20,139)( 21,133)( 22,134)( 23,136)( 24,135)( 25,129)( 26,130)( 27,132)( 28,131)( 29,125)( 30,126)( 31,128)( 32,127)( 33,121)( 34,122)( 35,124)( 36,123)( 37,117)( 38,118)( 39,120)( 40,119)( 41,113)( 42,114)( 43,116)( 44,115)( 45,109)( 46,110)( 47,112)( 48,111)( 49,105)( 50,106)( 51,108)( 52,107)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61, 93)( 62, 94)( 63, 96)( 64, 95)( 65, 89)( 66, 90)( 67, 92)( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 81)( 74, 82)( 75, 84)( 76, 83)( 79, 80);;
s2 := (  1,  4)(  2,  3)(  5,  8)(  6,  7)(  9, 12)( 10, 11)( 13, 16)( 14, 15)( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)( 33, 36)( 34, 35)( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)( 65, 68)( 66, 67)( 69, 72)( 70, 71)( 73, 76)( 74, 75)( 77, 80)( 78, 79)( 81, 84)( 82, 83)( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)( 94, 95)( 97,100)( 98, 99)(101,104)(102,103)(105,108)(106,107)(109,112)(110,111)(113,116)(114,115)(117,120)(118,119)(121,124)(122,123)(125,128)(126,127)(129,132)(130,131)(133,136)(134,135)(137,140)(138,139)(141,144)(142,143)(145,148)(146,147);;
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, 
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(148)!(  2,  3)(  5,145)(  6,147)(  7,146)(  8,148)(  9,141)( 10,143)( 11,142)( 12,144)( 13,137)( 14,139)( 15,138)( 16,140)( 17,133)( 18,135)( 19,134)( 20,136)( 21,129)( 22,131)( 23,130)( 24,132)( 25,125)( 26,127)( 27,126)( 28,128)( 29,121)( 30,123)( 31,122)( 32,124)( 33,117)( 34,119)( 35,118)( 36,120)( 37,113)( 38,115)( 39,114)( 40,116)( 41,109)( 42,111)( 43,110)( 44,112)( 45,105)( 46,107)( 47,106)( 48,108)( 49,101)( 50,103)( 51,102)( 52,104)( 53, 97)( 54, 99)( 55, 98)( 56,100)( 57, 93)( 58, 95)( 59, 94)( 60, 96)( 61, 89)( 62, 91)( 63, 90)( 64, 92)( 65, 85)( 66, 87)( 67, 86)( 68, 88)( 69, 81)( 70, 83)( 71, 82)( 72, 84)( 73, 77)( 74, 79)( 75, 78)( 76, 80);
s1 := Sym(148)!(  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9,145)( 10,146)( 11,148)( 12,147)( 13,141)( 14,142)( 15,144)( 16,143)( 17,137)( 18,138)( 19,140)( 20,139)( 21,133)( 22,134)( 23,136)( 24,135)( 25,129)( 26,130)( 27,132)( 28,131)( 29,125)( 30,126)( 31,128)( 32,127)( 33,121)( 34,122)( 35,124)( 36,123)( 37,117)( 38,118)( 39,120)( 40,119)( 41,113)( 42,114)( 43,116)( 44,115)( 45,109)( 46,110)( 47,112)( 48,111)( 49,105)( 50,106)( 51,108)( 52,107)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61, 93)( 62, 94)( 63, 96)( 64, 95)( 65, 89)( 66, 90)( 67, 92)( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 81)( 74, 82)( 75, 84)( 76, 83)( 79, 80);
s2 := Sym(148)!(  1,  4)(  2,  3)(  5,  8)(  6,  7)(  9, 12)( 10, 11)( 13, 16)( 14, 15)( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)( 33, 36)( 34, 35)( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)( 65, 68)( 66, 67)( 69, 72)( 70, 71)( 73, 76)( 74, 75)( 77, 80)( 78, 79)( 81, 84)( 82, 83)( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)( 94, 95)( 97,100)( 98, 99)(101,104)(102,103)(105,108)(106,107)(109,112)(110,111)(113,116)(114,115)(117,120)(118,119)(121,124)(122,123)(125,128)(126,127)(129,132)(130,131)(133,136)(134,135)(137,140)(138,139)(141,144)(142,143)(145,148)(146,147);
poly := sub<Sym(148)|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, 
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.

Twisty Puzzle