Polytope of Type {4,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,7}*1792b
if this polytope has a name.
Group : SmallGroup(1792,1083551)
Rank : 3
Schlafli Type : {4,7}
Number of vertices, edges, etc : 128, 448, 224
Order of s₀s₁s₂ : 14
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,7}*896
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope