Polytope of Type {10,4}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope