Polytope of Type {4,58}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,58}*464
Also Known As : {4,58|2}. if this polytope has another name.
Group : SmallGroup(464,39)
Rank : 3
Schlafli Type : {4,58}
Number of vertices, edges, etc : 4, 116, 58
Order of s₀s₁s₂ : 116
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,58,2} of size 928
   {4,58,4} of size 1856
Vertex Figure Of :
   {2,4,58} of size 928
   {4,4,58} of size 1856
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,58}*232
   4-fold quotients : {2,29}*116
   29-fold quotients : {4,2}*16
   58-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,116}*928, {8,58}*928
   3-fold covers : {12,58}*1392, {4,174}*1392a
   4-fold covers : {8,116}*1856a, {4,232}*1856a, {8,116}*1856b, {4,232}*1856b, {4,116}*1856, {16,58}*1856
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {4,58}

Twisty Puzzle