Polytope of Type {4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10}*1280a
if this polytope has a name.
Group : SmallGroup(1280,1116442)
Rank : 3
Schlafli Type : {4,10}
Number of vertices, edges, etc : 64, 320, 160
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,10}*640b
   4-fold quotients : {4,5}*320, {4,10}*320a, {4,10}*320b
   8-fold quotients : {4,5}*160
   16-fold quotients : {4,10}*80
   32-fold quotients : {2,10}*40
   64-fold quotients : {2,5}*20
   80-fold quotients : {4,2}*16
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope