Polytope of Type {2,8,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,16}*512c
if this polytope has a name.
Group : SmallGroup(512,396076)
Rank : 4
Schlafli Type : {2,8,16}
Number of vertices, edges, etc : 2, 8, 64, 16
Order of s₀s₁s₂s₃ : 16
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 : {2,8,8}*256a, {2,4,16}*256a
   4-fold quotients : {2,4,8}*128a, {2,8,4}*128b, {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, 45)( 12, 46)( 13, 43)( 14, 44)( 15, 49)( 16, 50)( 17, 47)( 18, 48)
( 19, 53)( 20, 54)( 21, 51)( 22, 52)( 23, 57)( 24, 58)( 25, 55)( 26, 56)
( 27, 59)( 28, 60)( 29, 61)( 30, 62)( 31, 63)( 32, 64)( 33, 65)( 34, 66)
( 67, 99)( 68,100)( 69,101)( 70,102)( 71,103)( 72,104)( 73,105)( 74,106)
( 75,109)( 76,110)( 77,107)( 78,108)( 79,113)( 80,114)( 81,111)( 82,112)
( 83,117)( 84,118)( 85,115)( 86,116)( 87,121)( 88,122)( 89,119)( 90,120)
( 91,123)( 92,124)( 93,125)( 94,126)( 95,127)( 96,128)( 97,129)( 98,130);;
s2 := (  7,  8)(  9, 10)( 11, 13)( 12, 14)( 15, 18)( 16, 17)( 19, 23)( 20, 24)
( 21, 25)( 22, 26)( 27, 33)( 28, 34)( 29, 31)( 30, 32)( 35, 43)( 36, 44)
( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 41, 50)( 42, 49)( 51, 63)( 52, 64)
( 53, 65)( 54, 66)( 55, 59)( 56, 60)( 57, 61)( 58, 62)( 67, 83)( 68, 84)
( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 90)( 74, 89)( 75, 93)( 76, 94)
( 77, 91)( 78, 92)( 79, 98)( 80, 97)( 81, 96)( 82, 95)( 99,125)(100,126)
(101,123)(102,124)(103,130)(104,129)(105,128)(106,127)(107,117)(108,118)
(109,115)(110,116)(111,122)(112,121)(113,120)(114,119);;
s3 := (  3, 67)(  4, 68)(  5, 69)(  6, 70)(  7, 72)(  8, 71)(  9, 74)( 10, 73)
( 11, 77)( 12, 78)( 13, 75)( 14, 76)( 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, 97)( 28, 98)( 29, 95)( 30, 96)( 31, 93)( 32, 94)( 33, 91)( 34, 92)
( 35, 99)( 36,100)( 37,101)( 38,102)( 39,104)( 40,103)( 41,106)( 42,105)
( 43,109)( 44,110)( 45,107)( 46,108)( 47,114)( 48,113)( 49,112)( 50,111)
( 51,119)( 52,120)( 53,121)( 54,122)( 55,115)( 56,116)( 57,117)( 58,118)
( 59,129)( 60,130)( 61,127)( 62,128)( 63,125)( 64,126)( 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*s1*s2*s3*s1*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*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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, 45)( 12, 46)( 13, 43)( 14, 44)( 15, 49)( 16, 50)( 17, 47)
( 18, 48)( 19, 53)( 20, 54)( 21, 51)( 22, 52)( 23, 57)( 24, 58)( 25, 55)
( 26, 56)( 27, 59)( 28, 60)( 29, 61)( 30, 62)( 31, 63)( 32, 64)( 33, 65)
( 34, 66)( 67, 99)( 68,100)( 69,101)( 70,102)( 71,103)( 72,104)( 73,105)
( 74,106)( 75,109)( 76,110)( 77,107)( 78,108)( 79,113)( 80,114)( 81,111)
( 82,112)( 83,117)( 84,118)( 85,115)( 86,116)( 87,121)( 88,122)( 89,119)
( 90,120)( 91,123)( 92,124)( 93,125)( 94,126)( 95,127)( 96,128)( 97,129)
( 98,130);
s2 := Sym(130)!(  7,  8)(  9, 10)( 11, 13)( 12, 14)( 15, 18)( 16, 17)( 19, 23)
( 20, 24)( 21, 25)( 22, 26)( 27, 33)( 28, 34)( 29, 31)( 30, 32)( 35, 43)
( 36, 44)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 41, 50)( 42, 49)( 51, 63)
( 52, 64)( 53, 65)( 54, 66)( 55, 59)( 56, 60)( 57, 61)( 58, 62)( 67, 83)
( 68, 84)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 90)( 74, 89)( 75, 93)
( 76, 94)( 77, 91)( 78, 92)( 79, 98)( 80, 97)( 81, 96)( 82, 95)( 99,125)
(100,126)(101,123)(102,124)(103,130)(104,129)(105,128)(106,127)(107,117)
(108,118)(109,115)(110,116)(111,122)(112,121)(113,120)(114,119);
s3 := Sym(130)!(  3, 67)(  4, 68)(  5, 69)(  6, 70)(  7, 72)(  8, 71)(  9, 74)
( 10, 73)( 11, 77)( 12, 78)( 13, 75)( 14, 76)( 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, 97)( 28, 98)( 29, 95)( 30, 96)( 31, 93)( 32, 94)( 33, 91)
( 34, 92)( 35, 99)( 36,100)( 37,101)( 38,102)( 39,104)( 40,103)( 41,106)
( 42,105)( 43,109)( 44,110)( 45,107)( 46,108)( 47,114)( 48,113)( 49,112)
( 50,111)( 51,119)( 52,120)( 53,121)( 54,122)( 55,115)( 56,116)( 57,117)
( 58,118)( 59,129)( 60,130)( 61,127)( 62,128)( 63,125)( 64,126)( 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*s1*s2*s3*s1*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*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope