Polytope of Type {2,4,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,8}*512a
if this polytope has a name.
Group : SmallGroup(512,6344662)
Rank : 5
Schlafli Type : {2,4,4,8}
Number of vertices, edges, etc : 2, 4, 8, 16, 8
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, {2,2,4,8}*256b
4-fold quotients : {2,2,4,4}*128, {2,4,4,2}*128, {2,4,2,4}*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, 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);;
s2 := ( 3, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 56)( 8, 55)( 9, 58)( 10, 57)
( 11, 60)( 12, 59)( 13, 62)( 14, 61)( 15, 63)( 16, 64)( 17, 65)( 18, 66)
( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 42)( 26, 41)
( 27, 44)( 28, 43)( 29, 46)( 30, 45)( 31, 47)( 32, 48)( 33, 49)( 34, 50)
( 67,115)( 68,116)( 69,117)( 70,118)( 71,120)( 72,119)( 73,122)( 74,121)
( 75,124)( 76,123)( 77,126)( 78,125)( 79,127)( 80,128)( 81,129)( 82,130)
( 83, 99)( 84,100)( 85,101)( 86,102)( 87,104)( 88,103)( 89,106)( 90,105)
( 91,108)( 92,107)( 93,110)( 94,109)( 95,111)( 96,112)( 97,113)( 98,114);;
s3 := ( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 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, 48)( 44, 47)( 45, 50)( 46, 49)( 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)( 91, 92)( 93, 94)
( 99,111)(100,112)(101,113)(102,114)(103,107)(104,108)(105,109)(106,110)
(115,119)(116,120)(117,121)(118,122)(123,128)(124,127)(125,130)(126,129);;
s4 := ( 3, 19)( 4, 20)( 5, 21)( 6, 22)( 7, 23)( 8, 24)( 9, 25)( 10, 26)
( 11, 28)( 12, 27)( 13, 30)( 14, 29)( 15, 32)( 16, 31)( 17, 34)( 18, 33)
( 35, 51)( 36, 52)( 37, 53)( 38, 54)( 39, 55)( 40, 56)( 41, 57)( 42, 58)
( 43, 60)( 44, 59)( 45, 62)( 46, 61)( 47, 64)( 48, 63)( 49, 66)( 50, 65)
( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)( 72, 88)( 73, 89)( 74, 90)
( 75, 92)( 76, 91)( 77, 94)( 78, 93)( 79, 96)( 80, 95)( 81, 98)( 82, 97)
( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)(105,121)(106,122)
(107,124)(108,123)(109,126)(110,125)(111,128)(112,127)(113,130)(114,129);;
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*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(130)!(1,2);
s1 := 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);
s2 := Sym(130)!( 3, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 56)( 8, 55)( 9, 58)
( 10, 57)( 11, 60)( 12, 59)( 13, 62)( 14, 61)( 15, 63)( 16, 64)( 17, 65)
( 18, 66)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 42)
( 26, 41)( 27, 44)( 28, 43)( 29, 46)( 30, 45)( 31, 47)( 32, 48)( 33, 49)
( 34, 50)( 67,115)( 68,116)( 69,117)( 70,118)( 71,120)( 72,119)( 73,122)
( 74,121)( 75,124)( 76,123)( 77,126)( 78,125)( 79,127)( 80,128)( 81,129)
( 82,130)( 83, 99)( 84,100)( 85,101)( 86,102)( 87,104)( 88,103)( 89,106)
( 90,105)( 91,108)( 92,107)( 93,110)( 94,109)( 95,111)( 96,112)( 97,113)
( 98,114);
s3 := Sym(130)!( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 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, 48)( 44, 47)( 45, 50)( 46, 49)( 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)( 91, 92)
( 93, 94)( 99,111)(100,112)(101,113)(102,114)(103,107)(104,108)(105,109)
(106,110)(115,119)(116,120)(117,121)(118,122)(123,128)(124,127)(125,130)
(126,129);
s4 := Sym(130)!( 3, 19)( 4, 20)( 5, 21)( 6, 22)( 7, 23)( 8, 24)( 9, 25)
( 10, 26)( 11, 28)( 12, 27)( 13, 30)( 14, 29)( 15, 32)( 16, 31)( 17, 34)
( 18, 33)( 35, 51)( 36, 52)( 37, 53)( 38, 54)( 39, 55)( 40, 56)( 41, 57)
( 42, 58)( 43, 60)( 44, 59)( 45, 62)( 46, 61)( 47, 64)( 48, 63)( 49, 66)
( 50, 65)( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)( 72, 88)( 73, 89)
( 74, 90)( 75, 92)( 76, 91)( 77, 94)( 78, 93)( 79, 96)( 80, 95)( 81, 98)
( 82, 97)( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)(105,121)
(106,122)(107,124)(108,123)(109,126)(110,125)(111,128)(112,127)(113,130)
(114,129);
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*s2*s3*s2*s3*s2*s3,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 >;
to this polytope