Polytope of Type {4,33,6} with group SmallGroup(1584,662)

Overview

Group: SmallGroup(1584,662)
Rank: 4
Schläfli Type: {4,33,6}
Vertices, edges, …: 4, 66, 99, 6
Order of s₀s₁s₂s₃: 66
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

3-fold

{4,33,2}*528

11-fold

{4,3,6}*144

33-fold

{4,3,2}*48

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132);;
s1 := (  3,  4)(  5, 41)(  6, 42)(  7, 44)(  8, 43)(  9, 37)( 10, 38)( 11, 40)( 12, 39)( 13, 33)( 14, 34)( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)( 45, 89)( 46, 90)( 47, 92)( 48, 91)( 49,129)( 50,130)( 51,132)( 52,131)( 53,125)( 54,126)( 55,128)( 56,127)( 57,121)( 58,122)( 59,124)( 60,123)( 61,117)( 62,118)( 63,120)( 64,119)( 65,113)( 66,114)( 67,116)( 68,115)( 69,109)( 70,110)( 71,112)( 72,111)( 73,105)( 74,106)( 75,108)( 76,107)( 77,101)( 78,102)( 79,104)( 80,103)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85, 93)( 86, 94)( 87, 96)( 88, 95);;
s2 := (  1, 49)(  2, 52)(  3, 51)(  4, 50)(  5, 45)(  6, 48)(  7, 47)(  8, 46)(  9, 85)( 10, 88)( 11, 87)( 12, 86)( 13, 81)( 14, 84)( 15, 83)( 16, 82)( 17, 77)( 18, 80)( 19, 79)( 20, 78)( 21, 73)( 22, 76)( 23, 75)( 24, 74)( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)( 32, 66)( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 37, 57)( 38, 60)( 39, 59)( 40, 58)( 41, 53)( 42, 56)( 43, 55)( 44, 54)( 89, 93)( 90, 96)( 91, 95)( 92, 94)( 97,129)( 98,132)( 99,131)(100,130)(101,125)(102,128)(103,127)(104,126)(105,121)(106,124)(107,123)(108,122)(109,117)(110,120)(111,119)(112,118)(114,116);;
s3 := ( 45, 89)( 46, 90)( 47, 91)( 48, 92)( 49, 93)( 50, 94)( 51, 95)( 52, 96)( 53, 97)( 54, 98)( 55, 99)( 56,100)( 57,101)( 58,102)( 59,103)( 60,104)( 61,105)( 62,106)( 63,107)( 64,108)( 65,109)( 66,110)( 67,111)( 68,112)( 69,113)( 70,114)( 71,115)( 72,116)( 73,117)( 74,118)( 75,119)( 76,120)( 77,121)( 78,122)( 79,123)( 80,124)( 81,125)( 82,126)( 83,127)( 84,128)( 85,129)( 86,130)( 87,131)( 88,132);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(132)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132);
s1 := Sym(132)!(  3,  4)(  5, 41)(  6, 42)(  7, 44)(  8, 43)(  9, 37)( 10, 38)( 11, 40)( 12, 39)( 13, 33)( 14, 34)( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)( 45, 89)( 46, 90)( 47, 92)( 48, 91)( 49,129)( 50,130)( 51,132)( 52,131)( 53,125)( 54,126)( 55,128)( 56,127)( 57,121)( 58,122)( 59,124)( 60,123)( 61,117)( 62,118)( 63,120)( 64,119)( 65,113)( 66,114)( 67,116)( 68,115)( 69,109)( 70,110)( 71,112)( 72,111)( 73,105)( 74,106)( 75,108)( 76,107)( 77,101)( 78,102)( 79,104)( 80,103)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85, 93)( 86, 94)( 87, 96)( 88, 95);
s2 := Sym(132)!(  1, 49)(  2, 52)(  3, 51)(  4, 50)(  5, 45)(  6, 48)(  7, 47)(  8, 46)(  9, 85)( 10, 88)( 11, 87)( 12, 86)( 13, 81)( 14, 84)( 15, 83)( 16, 82)( 17, 77)( 18, 80)( 19, 79)( 20, 78)( 21, 73)( 22, 76)( 23, 75)( 24, 74)( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)( 32, 66)( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 37, 57)( 38, 60)( 39, 59)( 40, 58)( 41, 53)( 42, 56)( 43, 55)( 44, 54)( 89, 93)( 90, 96)( 91, 95)( 92, 94)( 97,129)( 98,132)( 99,131)(100,130)(101,125)(102,128)(103,127)(104,126)(105,121)(106,124)(107,123)(108,122)(109,117)(110,120)(111,119)(112,118)(114,116);
s3 := Sym(132)!( 45, 89)( 46, 90)( 47, 91)( 48, 92)( 49, 93)( 50, 94)( 51, 95)( 52, 96)( 53, 97)( 54, 98)( 55, 99)( 56,100)( 57,101)( 58,102)( 59,103)( 60,104)( 61,105)( 62,106)( 63,107)( 64,108)( 65,109)( 66,110)( 67,111)( 68,112)( 69,113)( 70,114)( 71,115)( 72,116)( 73,117)( 74,118)( 75,119)( 76,120)( 77,121)( 78,122)( 79,123)( 80,124)( 81,125)( 82,126)( 83,127)( 84,128)( 85,129)( 86,130)( 87,131)( 88,132);
poly := sub<Sym(132)|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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*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*s1*s2*s1*s2 >;

References