Polytope of Type {2,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,4}*512a
if this polytope has a name.
Group : SmallGroup(512,391345)
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 : {2,8,4}*256a, {2,4,4}*256, {2,8,4}*256b
   4-fold quotients : {2,8,4}*128a, {2,8,4}*128b, {2,4,4}*128
   8-fold quotients : {2,4,4}*64, {2,8,2}*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, 69)(  6, 70)(  7, 71)(  8, 72)(  9, 73)( 10, 74)
( 11, 78)( 12, 77)( 13, 76)( 14, 75)( 15, 82)( 16, 81)( 17, 80)( 18, 79)
( 19, 87)( 20, 88)( 21, 89)( 22, 90)( 23, 83)( 24, 84)( 25, 85)( 26, 86)
( 27, 98)( 28, 97)( 29, 96)( 30, 95)( 31, 94)( 32, 93)( 33, 92)( 34, 91)
( 35, 99)( 36,100)( 37,101)( 38,102)( 39,103)( 40,104)( 41,105)( 42,106)
( 43,110)( 44,109)( 45,108)( 46,107)( 47,114)( 48,113)( 49,112)( 50,111)
( 51,119)( 52,120)( 53,121)( 54,122)( 55,115)( 56,116)( 57,117)( 58,118)
( 59,130)( 60,129)( 61,128)( 62,127)( 63,126)( 64,125)( 65,124)( 66,123);;
s2 := (  5,  6)(  9, 10)( 13, 14)( 17, 18)( 19, 23)( 20, 24)( 21, 26)( 22, 25)
( 27, 31)( 28, 32)( 29, 34)( 30, 33)( 35, 43)( 36, 44)( 37, 46)( 38, 45)
( 39, 47)( 40, 48)( 41, 50)( 42, 49)( 51, 64)( 52, 63)( 53, 65)( 54, 66)
( 55, 60)( 56, 59)( 57, 61)( 58, 62)( 67, 83)( 68, 84)( 69, 86)( 70, 85)
( 71, 87)( 72, 88)( 73, 90)( 74, 89)( 75, 91)( 76, 92)( 77, 94)( 78, 93)
( 79, 95)( 80, 96)( 81, 98)( 82, 97)( 99,125)(100,126)(101,124)(102,123)
(103,129)(104,130)(105,128)(106,127)(107,117)(108,118)(109,116)(110,115)
(111,121)(112,122)(113,120)(114,119);;
s3 := (  3, 35)(  4, 36)(  5, 37)(  6, 38)(  7, 39)(  8, 40)(  9, 41)( 10, 42)
( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 47)( 16, 48)( 17, 49)( 18, 50)
( 19, 53)( 20, 54)( 21, 51)( 22, 52)( 23, 57)( 24, 58)( 25, 55)( 26, 56)
( 27, 61)( 28, 62)( 29, 59)( 30, 60)( 31, 65)( 32, 66)( 33, 63)( 34, 64)
( 67, 99)( 68,100)( 69,101)( 70,102)( 71,103)( 72,104)( 73,105)( 74,106)
( 75,107)( 76,108)( 77,109)( 78,110)( 79,111)( 80,112)( 81,113)( 82,114)
( 83,117)( 84,118)( 85,115)( 86,116)( 87,121)( 88,122)( 89,119)( 90,120)
( 91,125)( 92,126)( 93,123)( 94,124)( 95,129)( 96,130)( 97,127)( 98,128);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope