Polytope of Type {2,8,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,8}*512h
if this polytope has a name.
Group : SmallGroup(512,420085)
Rank : 4
Schlafli Type : {2,8,8}
Number of vertices, edges, etc : 2, 16, 64, 16
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,8,4}*256b
   4-fold quotients : {2,4,4}*128
   8-fold quotients : {2,4,4}*64
   16-fold quotients : {2,2,4}*32, {2,4,2}*32
   32-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  3, 99)(  4,100)(  5,101)(  6,102)(  7,104)(  8,103)(  9,106)( 10,105)
( 11,113)( 12,114)( 13,111)( 14,112)( 15,109)( 16,110)( 17,107)( 18,108)
( 19,120)( 20,119)( 21,122)( 22,121)( 23,116)( 24,115)( 25,118)( 26,117)
( 27,126)( 28,125)( 29,124)( 30,123)( 31,129)( 32,130)( 33,127)( 34,128)
( 35, 67)( 36, 68)( 37, 69)( 38, 70)( 39, 72)( 40, 71)( 41, 74)( 42, 73)
( 43, 81)( 44, 82)( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 75)( 50, 76)
( 51, 88)( 52, 87)( 53, 90)( 54, 89)( 55, 84)( 56, 83)( 57, 86)( 58, 85)
( 59, 94)( 60, 93)( 61, 92)( 62, 91)( 63, 97)( 64, 98)( 65, 95)( 66, 96);;
s2 := (  7,  9)(  8, 10)( 11, 12)( 13, 14)( 15, 18)( 16, 17)( 19, 20)( 21, 22)
( 23, 26)( 24, 25)( 31, 33)( 32, 34)( 35, 43)( 36, 44)( 37, 45)( 38, 46)
( 39, 49)( 40, 50)( 41, 47)( 42, 48)( 51, 61)( 52, 62)( 53, 59)( 54, 60)
( 55, 63)( 56, 64)( 57, 65)( 58, 66)( 67, 83)( 68, 84)( 69, 85)( 70, 86)
( 71, 89)( 72, 90)( 73, 87)( 74, 88)( 75, 92)( 76, 91)( 77, 94)( 78, 93)
( 79, 98)( 80, 97)( 81, 96)( 82, 95)( 99,128)(100,127)(101,130)(102,129)
(103,125)(104,126)(105,123)(106,124)(107,119)(108,120)(109,121)(110,122)
(111,118)(112,117)(113,116)(114,115);;
s3 := (  3, 67)(  4, 68)(  5, 70)(  6, 69)(  7, 71)(  8, 72)(  9, 74)( 10, 73)
( 11, 82)( 12, 81)( 13, 79)( 14, 80)( 15, 77)( 16, 78)( 17, 76)( 18, 75)
( 19, 84)( 20, 83)( 21, 85)( 22, 86)( 23, 88)( 24, 87)( 25, 89)( 26, 90)
( 27, 97)( 28, 98)( 29, 96)( 30, 95)( 31, 94)( 32, 93)( 33, 91)( 34, 92)
( 35, 99)( 36,100)( 37,102)( 38,101)( 39,103)( 40,104)( 41,106)( 42,105)
( 43,114)( 44,113)( 45,111)( 46,112)( 47,109)( 48,110)( 49,108)( 50,107)
( 51,116)( 52,115)( 53,117)( 54,118)( 55,120)( 56,119)( 57,121)( 58,122)
( 59,129)( 60,130)( 61,128)( 62,127)( 63,126)( 64,125)( 65,123)( 66,124);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(130)!(1,2);
s1 := Sym(130)!(  3, 99)(  4,100)(  5,101)(  6,102)(  7,104)(  8,103)(  9,106)
( 10,105)( 11,113)( 12,114)( 13,111)( 14,112)( 15,109)( 16,110)( 17,107)
( 18,108)( 19,120)( 20,119)( 21,122)( 22,121)( 23,116)( 24,115)( 25,118)
( 26,117)( 27,126)( 28,125)( 29,124)( 30,123)( 31,129)( 32,130)( 33,127)
( 34,128)( 35, 67)( 36, 68)( 37, 69)( 38, 70)( 39, 72)( 40, 71)( 41, 74)
( 42, 73)( 43, 81)( 44, 82)( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 75)
( 50, 76)( 51, 88)( 52, 87)( 53, 90)( 54, 89)( 55, 84)( 56, 83)( 57, 86)
( 58, 85)( 59, 94)( 60, 93)( 61, 92)( 62, 91)( 63, 97)( 64, 98)( 65, 95)
( 66, 96);
s2 := Sym(130)!(  7,  9)(  8, 10)( 11, 12)( 13, 14)( 15, 18)( 16, 17)( 19, 20)
( 21, 22)( 23, 26)( 24, 25)( 31, 33)( 32, 34)( 35, 43)( 36, 44)( 37, 45)
( 38, 46)( 39, 49)( 40, 50)( 41, 47)( 42, 48)( 51, 61)( 52, 62)( 53, 59)
( 54, 60)( 55, 63)( 56, 64)( 57, 65)( 58, 66)( 67, 83)( 68, 84)( 69, 85)
( 70, 86)( 71, 89)( 72, 90)( 73, 87)( 74, 88)( 75, 92)( 76, 91)( 77, 94)
( 78, 93)( 79, 98)( 80, 97)( 81, 96)( 82, 95)( 99,128)(100,127)(101,130)
(102,129)(103,125)(104,126)(105,123)(106,124)(107,119)(108,120)(109,121)
(110,122)(111,118)(112,117)(113,116)(114,115);
s3 := Sym(130)!(  3, 67)(  4, 68)(  5, 70)(  6, 69)(  7, 71)(  8, 72)(  9, 74)
( 10, 73)( 11, 82)( 12, 81)( 13, 79)( 14, 80)( 15, 77)( 16, 78)( 17, 76)
( 18, 75)( 19, 84)( 20, 83)( 21, 85)( 22, 86)( 23, 88)( 24, 87)( 25, 89)
( 26, 90)( 27, 97)( 28, 98)( 29, 96)( 30, 95)( 31, 94)( 32, 93)( 33, 91)
( 34, 92)( 35, 99)( 36,100)( 37,102)( 38,101)( 39,103)( 40,104)( 41,106)
( 42,105)( 43,114)( 44,113)( 45,111)( 46,112)( 47,109)( 48,110)( 49,108)
( 50,107)( 51,116)( 52,115)( 53,117)( 54,118)( 55,120)( 56,119)( 57,121)
( 58,122)( 59,129)( 60,130)( 61,128)( 62,127)( 63,126)( 64,125)( 65,123)
( 66,124);
poly := sub<Sym(130)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3 >;

to this polytope