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Polytope of Type {4,32,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,32,2}*512a
if this polytope has a name.
Group : SmallGroup(512,420016)
Rank : 4
Schlafli Type : {4,32,2}
Number of vertices, edges, etc : 4, 64, 32, 2
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 : {4,16,2}*256a, {2,32,2}*256
4-fold quotients : {4,8,2}*128a, {2,16,2}*128
8-fold quotients : {4,4,2}*64, {2,8,2}*64
16-fold quotients : {2,4,2}*32, {4,2,2}*32
32-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 33)( 2, 34)( 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, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 55)( 24, 56)
( 25, 57)( 26, 58)( 27, 59)( 28, 60)( 29, 61)( 30, 62)( 31, 63)( 32, 64)
( 65, 97)( 66, 98)( 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)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)( 88,120)
( 89,121)( 90,122)( 91,123)( 92,124)( 93,125)( 94,126)( 95,127)( 96,128);;
s1 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 17, 21)( 18, 22)
( 19, 24)( 20, 23)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 33, 41)( 34, 42)
( 35, 44)( 36, 43)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 49, 61)( 50, 62)
( 51, 64)( 52, 63)( 53, 57)( 54, 58)( 55, 60)( 56, 59)( 65, 81)( 66, 82)
( 67, 84)( 68, 83)( 69, 87)( 70, 88)( 71, 85)( 72, 86)( 73, 89)( 74, 90)
( 75, 92)( 76, 91)( 77, 95)( 78, 96)( 79, 93)( 80, 94)( 97,121)( 98,122)
( 99,124)(100,123)(101,127)(102,128)(103,125)(104,126)(105,113)(106,114)
(107,116)(108,115)(109,119)(110,120)(111,117)(112,118);;
s2 := ( 1, 65)( 2, 66)( 3, 68)( 4, 67)( 5, 71)( 6, 72)( 7, 69)( 8, 70)
( 9, 73)( 10, 74)( 11, 76)( 12, 75)( 13, 79)( 14, 80)( 15, 77)( 16, 78)
( 17, 85)( 18, 86)( 19, 88)( 20, 87)( 21, 81)( 22, 82)( 23, 84)( 24, 83)
( 25, 93)( 26, 94)( 27, 96)( 28, 95)( 29, 89)( 30, 90)( 31, 92)( 32, 91)
( 33, 97)( 34, 98)( 35,100)( 36, 99)( 37,103)( 38,104)( 39,101)( 40,102)
( 41,105)( 42,106)( 43,108)( 44,107)( 45,111)( 46,112)( 47,109)( 48,110)
( 49,117)( 50,118)( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)( 56,115)
( 57,125)( 58,126)( 59,128)( 60,127)( 61,121)( 62,122)( 63,124)( 64,123);;
s3 := (129,130);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
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*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, 33)( 2, 34)( 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, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 55)
( 24, 56)( 25, 57)( 26, 58)( 27, 59)( 28, 60)( 29, 61)( 30, 62)( 31, 63)
( 32, 64)( 65, 97)( 66, 98)( 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)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)
( 88,120)( 89,121)( 90,122)( 91,123)( 92,124)( 93,125)( 94,126)( 95,127)
( 96,128);
s1 := Sym(130)!( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 17, 21)
( 18, 22)( 19, 24)( 20, 23)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 33, 41)
( 34, 42)( 35, 44)( 36, 43)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 49, 61)
( 50, 62)( 51, 64)( 52, 63)( 53, 57)( 54, 58)( 55, 60)( 56, 59)( 65, 81)
( 66, 82)( 67, 84)( 68, 83)( 69, 87)( 70, 88)( 71, 85)( 72, 86)( 73, 89)
( 74, 90)( 75, 92)( 76, 91)( 77, 95)( 78, 96)( 79, 93)( 80, 94)( 97,121)
( 98,122)( 99,124)(100,123)(101,127)(102,128)(103,125)(104,126)(105,113)
(106,114)(107,116)(108,115)(109,119)(110,120)(111,117)(112,118);
s2 := Sym(130)!( 1, 65)( 2, 66)( 3, 68)( 4, 67)( 5, 71)( 6, 72)( 7, 69)
( 8, 70)( 9, 73)( 10, 74)( 11, 76)( 12, 75)( 13, 79)( 14, 80)( 15, 77)
( 16, 78)( 17, 85)( 18, 86)( 19, 88)( 20, 87)( 21, 81)( 22, 82)( 23, 84)
( 24, 83)( 25, 93)( 26, 94)( 27, 96)( 28, 95)( 29, 89)( 30, 90)( 31, 92)
( 32, 91)( 33, 97)( 34, 98)( 35,100)( 36, 99)( 37,103)( 38,104)( 39,101)
( 40,102)( 41,105)( 42,106)( 43,108)( 44,107)( 45,111)( 46,112)( 47,109)
( 48,110)( 49,117)( 50,118)( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)
( 56,115)( 57,125)( 58,126)( 59,128)( 60,127)( 61,121)( 62,122)( 63,124)
( 64,123);
s3 := Sym(130)!(129,130);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, 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*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 >;
to this polytope