Polytope of Type {2,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,4}*512c
if this polytope has a name.
Group : SmallGroup(512,420067)
Rank : 4
Schlafli Type : {2,8,4}
Number of vertices, edges, etc : 2, 32, 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 : {2,4,4}*256
   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, 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);;
s2 := (  7,  9)(  8, 10)( 15, 17)( 16, 18)( 19, 20)( 21, 22)( 23, 26)( 24, 25)
( 27, 28)( 29, 30)( 31, 34)( 32, 33)( 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, 91)( 76, 92)( 77, 93)( 78, 94)
( 79, 97)( 80, 98)( 81, 95)( 82, 96)( 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, 35)(  4, 36)(  5, 38)(  6, 37)(  7, 40)(  8, 39)(  9, 41)( 10, 42)
( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 48)( 16, 47)( 17, 49)( 18, 50)
( 19, 55)( 20, 56)( 21, 58)( 22, 57)( 23, 51)( 24, 52)( 25, 54)( 26, 53)
( 27, 64)( 28, 63)( 29, 65)( 30, 66)( 31, 60)( 32, 59)( 33, 61)( 34, 62)
( 67, 99)( 68,100)( 69,102)( 70,101)( 71,104)( 72,103)( 73,105)( 74,106)
( 75,107)( 76,108)( 77,110)( 78,109)( 79,112)( 80,111)( 81,113)( 82,114)
( 83,119)( 84,120)( 85,122)( 86,121)( 87,115)( 88,116)( 89,118)( 90,117)
( 91,128)( 92,127)( 93,129)( 94,130)( 95,124)( 96,123)( 97,125)( 98,126);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s2*s1*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope