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Polytope of Type {2,4,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,8,4}*512a
if this polytope has a name.
Group : SmallGroup(512,6344594)
Rank : 5
Schlafli Type : {2,4,8,4}
Number of vertices, edges, etc : 2, 4, 16, 16, 4
Order of s0s1s2s3s4 : 8
Order of s0s1s2s3s4s3s2s1 : 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 : {2,4,4,4}*256, {2,2,8,4}*256a, {2,4,8,2}*256a
   4-fold quotients : {2,2,4,4}*128, {2,4,4,2}*128, {2,4,2,4}*128, {2,2,8,2}*128
   8-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64, {2,4,2,2}*64
   16-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3, 19)(  4, 20)(  5, 21)(  6, 22)(  7, 23)(  8, 24)(  9, 25)( 10, 26)
( 11, 27)( 12, 28)( 13, 29)( 14, 30)( 15, 31)( 16, 32)( 17, 33)( 18, 34)
( 35, 51)( 36, 52)( 37, 53)( 38, 54)( 39, 55)( 40, 56)( 41, 57)( 42, 58)
( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)( 48, 64)( 49, 65)( 50, 66)
( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)( 72, 88)( 73, 89)( 74, 90)
( 75, 91)( 76, 92)( 77, 93)( 78, 94)( 79, 95)( 80, 96)( 81, 97)( 82, 98)
( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)(105,121)(106,122)
(107,123)(108,124)(109,125)(110,126)(111,127)(112,128)(113,129)(114,130);;
s2 := (  7,  8)(  9, 10)( 15, 16)( 17, 18)( 19, 27)( 20, 28)( 21, 29)( 22, 30)
( 23, 32)( 24, 31)( 25, 34)( 26, 33)( 35, 39)( 36, 40)( 37, 41)( 38, 42)
( 43, 47)( 44, 48)( 45, 49)( 46, 50)( 51, 63)( 52, 64)( 53, 65)( 54, 66)
( 55, 59)( 56, 60)( 57, 61)( 58, 62)( 67, 75)( 68, 76)( 69, 77)( 70, 78)
( 71, 80)( 72, 79)( 73, 82)( 74, 81)( 87, 88)( 89, 90)( 95, 96)( 97, 98)
( 99,111)(100,112)(101,113)(102,114)(103,107)(104,108)(105,109)(106,110)
(115,119)(116,120)(117,121)(118,122)(123,127)(124,128)(125,129)(126,130);;
s3 := (  3, 35)(  4, 36)(  5, 37)(  6, 38)(  7, 40)(  8, 39)(  9, 42)( 10, 41)
( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 48)( 16, 47)( 17, 50)( 18, 49)
( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 56)( 24, 55)( 25, 58)( 26, 57)
( 27, 59)( 28, 60)( 29, 61)( 30, 62)( 31, 64)( 32, 63)( 33, 66)( 34, 65)
( 67, 99)( 68,100)( 69,101)( 70,102)( 71,104)( 72,103)( 73,106)( 74,105)
( 75,107)( 76,108)( 77,109)( 78,110)( 79,112)( 80,111)( 81,114)( 82,113)
( 83,115)( 84,116)( 85,117)( 86,118)( 87,120)( 88,119)( 89,122)( 90,121)
( 91,123)( 92,124)( 93,125)( 94,126)( 95,128)( 96,127)( 97,130)( 98,129);;
s4 := (  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)(  8, 88)(  9, 89)( 10, 90)
( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)( 17, 97)( 18, 98)
( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)( 24, 72)( 25, 73)( 26, 74)
( 27, 75)( 28, 76)( 29, 77)( 30, 78)( 31, 79)( 32, 80)( 33, 81)( 34, 82)
( 35,117)( 36,118)( 37,115)( 38,116)( 39,121)( 40,122)( 41,119)( 42,120)
( 43,125)( 44,126)( 45,123)( 46,124)( 47,129)( 48,130)( 49,127)( 50,128)
( 51,101)( 52,102)( 53, 99)( 54,100)( 55,105)( 56,106)( 57,103)( 58,104)
( 59,109)( 60,110)( 61,107)( 62,108)( 63,113)( 64,114)( 65,111)( 66,112);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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, 19)(  4, 20)(  5, 21)(  6, 22)(  7, 23)(  8, 24)(  9, 25)
( 10, 26)( 11, 27)( 12, 28)( 13, 29)( 14, 30)( 15, 31)( 16, 32)( 17, 33)
( 18, 34)( 35, 51)( 36, 52)( 37, 53)( 38, 54)( 39, 55)( 40, 56)( 41, 57)
( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)( 48, 64)( 49, 65)
( 50, 66)( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)( 72, 88)( 73, 89)
( 74, 90)( 75, 91)( 76, 92)( 77, 93)( 78, 94)( 79, 95)( 80, 96)( 81, 97)
( 82, 98)( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)(105,121)
(106,122)(107,123)(108,124)(109,125)(110,126)(111,127)(112,128)(113,129)
(114,130);
s2 := Sym(130)!(  7,  8)(  9, 10)( 15, 16)( 17, 18)( 19, 27)( 20, 28)( 21, 29)
( 22, 30)( 23, 32)( 24, 31)( 25, 34)( 26, 33)( 35, 39)( 36, 40)( 37, 41)
( 38, 42)( 43, 47)( 44, 48)( 45, 49)( 46, 50)( 51, 63)( 52, 64)( 53, 65)
( 54, 66)( 55, 59)( 56, 60)( 57, 61)( 58, 62)( 67, 75)( 68, 76)( 69, 77)
( 70, 78)( 71, 80)( 72, 79)( 73, 82)( 74, 81)( 87, 88)( 89, 90)( 95, 96)
( 97, 98)( 99,111)(100,112)(101,113)(102,114)(103,107)(104,108)(105,109)
(106,110)(115,119)(116,120)(117,121)(118,122)(123,127)(124,128)(125,129)
(126,130);
s3 := Sym(130)!(  3, 35)(  4, 36)(  5, 37)(  6, 38)(  7, 40)(  8, 39)(  9, 42)
( 10, 41)( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 48)( 16, 47)( 17, 50)
( 18, 49)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 56)( 24, 55)( 25, 58)
( 26, 57)( 27, 59)( 28, 60)( 29, 61)( 30, 62)( 31, 64)( 32, 63)( 33, 66)
( 34, 65)( 67, 99)( 68,100)( 69,101)( 70,102)( 71,104)( 72,103)( 73,106)
( 74,105)( 75,107)( 76,108)( 77,109)( 78,110)( 79,112)( 80,111)( 81,114)
( 82,113)( 83,115)( 84,116)( 85,117)( 86,118)( 87,120)( 88,119)( 89,122)
( 90,121)( 91,123)( 92,124)( 93,125)( 94,126)( 95,128)( 96,127)( 97,130)
( 98,129);
s4 := Sym(130)!(  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)(  8, 88)(  9, 89)
( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)( 17, 97)
( 18, 98)( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)( 24, 72)( 25, 73)
( 26, 74)( 27, 75)( 28, 76)( 29, 77)( 30, 78)( 31, 79)( 32, 80)( 33, 81)
( 34, 82)( 35,117)( 36,118)( 37,115)( 38,116)( 39,121)( 40,122)( 41,119)
( 42,120)( 43,125)( 44,126)( 45,123)( 46,124)( 47,129)( 48,130)( 49,127)
( 50,128)( 51,101)( 52,102)( 53, 99)( 54,100)( 55,105)( 56,106)( 57,103)
( 58,104)( 59,109)( 60,110)( 61,107)( 62,108)( 63,113)( 64,114)( 65,111)
( 66,112);
poly := sub<Sym(130)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

to this polytope