Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,16,8}

Atlas Canonical Name {2,16,8}*512d

Overview

Group
SmallGroup(512,396076)
Rank
4
Schläfli Type
{2,16,8}
Vertices, edges, …
2, 16, 64, 8
Order of s0s1s2s3
16
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

32-fold

Covers minimal covers in bold

None in this atlas.

Representations

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