Polytope of Type {2,4,32}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,32}*512b
if this polytope has a name.
Group : SmallGroup(512,420034)
Rank : 4
Schlafli Type : {2,4,32}
Number of vertices, edges, etc : 2, 4, 64, 32
Order of s₀s₁s₂s₃ : 32
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 : {2,4,16}*256a
   4-fold quotients : {2,4,8}*128a, {2,2,16}*128
   8-fold quotients : {2,4,4}*64, {2,2,8}*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, 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, 52)( 20, 51)( 21, 54)( 22, 53)( 23, 56)( 24, 55)( 25, 58)( 26, 57)
( 27, 60)( 28, 59)( 29, 62)( 30, 61)( 31, 64)( 32, 63)( 33, 66)( 34, 65)
( 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)
( 83,116)( 84,115)( 85,118)( 86,117)( 87,120)( 88,119)( 89,122)( 90,121)
( 91,124)( 92,123)( 93,126)( 94,125)( 95,128)( 96,127)( 97,130)( 98,129);;
s2 := (  5,  6)(  7,  9)(  8, 10)( 13, 14)( 15, 17)( 16, 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, 49)( 40, 50)( 41, 47)( 42, 48)( 51, 63)( 52, 64)
( 53, 66)( 54, 65)( 55, 59)( 56, 60)( 57, 62)( 58, 61)( 67, 83)( 68, 84)
( 69, 86)( 70, 85)( 71, 89)( 72, 90)( 73, 87)( 74, 88)( 75, 91)( 76, 92)
( 77, 94)( 78, 93)( 79, 97)( 80, 98)( 81, 95)( 82, 96)( 99,124)(100,123)
(101,125)(102,126)(103,130)(104,129)(105,128)(106,127)(107,116)(108,115)
(109,117)(110,118)(111,122)(112,121)(113,120)(114,119);;
s3 := (  3, 67)(  4, 68)(  5, 70)(  6, 69)(  7, 73)(  8, 74)(  9, 71)( 10, 72)
( 11, 76)( 12, 75)( 13, 77)( 14, 78)( 15, 82)( 16, 81)( 17, 80)( 18, 79)
( 19, 87)( 20, 88)( 21, 90)( 22, 89)( 23, 83)( 24, 84)( 25, 86)( 26, 85)
( 27, 96)( 28, 95)( 29, 97)( 30, 98)( 31, 92)( 32, 91)( 33, 93)( 34, 94)
( 35, 99)( 36,100)( 37,102)( 38,101)( 39,105)( 40,106)( 41,103)( 42,104)
( 43,108)( 44,107)( 45,109)( 46,110)( 47,114)( 48,113)( 49,112)( 50,111)
( 51,119)( 52,120)( 53,122)( 54,121)( 55,115)( 56,116)( 57,118)( 58,117)
( 59,128)( 60,127)( 61,129)( 62,130)( 63,124)( 64,123)( 65,125)( 66,126);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope