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Polytope of Type {14,7}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,7}*1792a
if this polytope has a name.
Group : SmallGroup(1792,1083551)
Rank : 3
Schlafli Type : {14,7}
Number of vertices, edges, etc : 128, 448, 64
Order of s0s1s2 : 8
Order of s0s1s2s1 : 7
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {7,7}*896
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 17)( 4, 18)( 5, 97)( 6, 98)( 7,113)( 8,114)( 9, 33)( 10, 34)
( 11, 49)( 12, 50)( 13, 65)( 14, 66)( 15, 81)( 16, 82)( 19, 20)( 21,100)
( 22, 99)( 23,115)( 24,116)( 25, 36)( 26, 35)( 27, 51)( 28, 52)( 29, 67)
( 30, 68)( 31, 84)( 32, 83)( 37,105)( 38,106)( 39,122)( 40,121)( 43, 58)
( 44, 57)( 45, 73)( 46, 74)( 47, 90)( 48, 89)( 53,108)( 54,107)( 55,124)
( 56,123)( 59, 60)( 61, 75)( 62, 76)( 63, 91)( 64, 92)( 69,110)( 70,109)
( 71,126)( 72,125)( 77, 78)( 79, 94)( 80, 93)( 85,111)( 86,112)( 87,128)
( 88,127)(101,102)(103,117)(104,118);;
s1 := ( 1, 2)( 3, 34)( 4, 33)( 5,114)( 6,113)( 7, 82)( 8, 81)( 9, 66)
( 10, 65)( 11, 98)( 12, 97)( 13, 50)( 14, 49)( 15, 18)( 16, 17)( 19, 47)
( 20, 48)( 21,127)( 22,128)( 23, 96)( 24, 95)( 25, 79)( 26, 80)( 27,112)
( 28,111)( 29, 64)( 30, 63)( 37,116)( 38,115)( 39, 83)( 40, 84)( 41, 68)
( 42, 67)( 43, 99)( 44,100)( 45, 52)( 46, 51)( 53,125)( 54,126)( 55, 93)
( 56, 94)( 57, 77)( 58, 78)( 59,109)( 60,110)( 61, 62)( 69,121)( 70,122)
( 71, 89)( 72, 90)( 73, 74)( 75,106)( 76,105)( 85,120)( 86,119)( 91,104)
( 92,103)(101,123)(102,124)(117,118);;
s2 := ( 1, 41)( 2, 42)( 3, 57)( 4, 58)( 5, 73)( 6, 74)( 7, 89)( 8, 90)
( 11, 25)( 12, 26)( 13,105)( 14,106)( 15,121)( 16,122)( 17, 44)( 18, 43)
( 19, 59)( 20, 60)( 21, 75)( 22, 76)( 23, 92)( 24, 91)( 27, 28)( 29,108)
( 30,107)( 31,123)( 32,124)( 35, 50)( 36, 49)( 37, 65)( 38, 66)( 39, 82)
( 40, 81)( 45, 97)( 46, 98)( 47,114)( 48,113)( 51, 52)( 53, 67)( 54, 68)
( 55, 83)( 56, 84)( 61,100)( 62, 99)( 63,116)( 64,115)( 69, 70)( 71, 86)
( 72, 85)( 77,102)( 78,101)( 79,118)( 80,117)( 93,103)( 94,104)( 95,120)
( 96,119)(109,110)(111,125)(112,126);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(128)!( 3, 17)( 4, 18)( 5, 97)( 6, 98)( 7,113)( 8,114)( 9, 33)
( 10, 34)( 11, 49)( 12, 50)( 13, 65)( 14, 66)( 15, 81)( 16, 82)( 19, 20)
( 21,100)( 22, 99)( 23,115)( 24,116)( 25, 36)( 26, 35)( 27, 51)( 28, 52)
( 29, 67)( 30, 68)( 31, 84)( 32, 83)( 37,105)( 38,106)( 39,122)( 40,121)
( 43, 58)( 44, 57)( 45, 73)( 46, 74)( 47, 90)( 48, 89)( 53,108)( 54,107)
( 55,124)( 56,123)( 59, 60)( 61, 75)( 62, 76)( 63, 91)( 64, 92)( 69,110)
( 70,109)( 71,126)( 72,125)( 77, 78)( 79, 94)( 80, 93)( 85,111)( 86,112)
( 87,128)( 88,127)(101,102)(103,117)(104,118);
s1 := Sym(128)!( 1, 2)( 3, 34)( 4, 33)( 5,114)( 6,113)( 7, 82)( 8, 81)
( 9, 66)( 10, 65)( 11, 98)( 12, 97)( 13, 50)( 14, 49)( 15, 18)( 16, 17)
( 19, 47)( 20, 48)( 21,127)( 22,128)( 23, 96)( 24, 95)( 25, 79)( 26, 80)
( 27,112)( 28,111)( 29, 64)( 30, 63)( 37,116)( 38,115)( 39, 83)( 40, 84)
( 41, 68)( 42, 67)( 43, 99)( 44,100)( 45, 52)( 46, 51)( 53,125)( 54,126)
( 55, 93)( 56, 94)( 57, 77)( 58, 78)( 59,109)( 60,110)( 61, 62)( 69,121)
( 70,122)( 71, 89)( 72, 90)( 73, 74)( 75,106)( 76,105)( 85,120)( 86,119)
( 91,104)( 92,103)(101,123)(102,124)(117,118);
s2 := Sym(128)!( 1, 41)( 2, 42)( 3, 57)( 4, 58)( 5, 73)( 6, 74)( 7, 89)
( 8, 90)( 11, 25)( 12, 26)( 13,105)( 14,106)( 15,121)( 16,122)( 17, 44)
( 18, 43)( 19, 59)( 20, 60)( 21, 75)( 22, 76)( 23, 92)( 24, 91)( 27, 28)
( 29,108)( 30,107)( 31,123)( 32,124)( 35, 50)( 36, 49)( 37, 65)( 38, 66)
( 39, 82)( 40, 81)( 45, 97)( 46, 98)( 47,114)( 48,113)( 51, 52)( 53, 67)
( 54, 68)( 55, 83)( 56, 84)( 61,100)( 62, 99)( 63,116)( 64,115)( 69, 70)
( 71, 86)( 72, 85)( 77,102)( 78,101)( 79,118)( 80,117)( 93,103)( 94,104)
( 95,120)( 96,119)(109,110)(111,125)(112,126);
poly := sub<Sym(128)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1 >;
References : None.
to this polytope