Polytope of Type {20,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,10}*1280d
if this polytope has a name.
Group : SmallGroup(1280,1116454)
Rank : 3
Schlafli Type : {20,10}
Number of vertices, edges, etc : 64, 320, 32
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,5}*640b, {10,10}*640d
   4-fold quotients : {5,10}*320b, {10,5}*320b
   8-fold quotients : {5,5}*160
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope