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Polytope of Type {50,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {50,4}*400
Also Known As : {50,4|2}. if this polytope has another name.
Group : SmallGroup(400,39)
Rank : 3
Schlafli Type : {50,4}
Number of vertices, edges, etc : 50, 100, 4
Order of s0s1s2 : 100
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {50,4,2} of size 800
   {50,4,4} of size 1600
Vertex Figure Of :
   {2,50,4} of size 800
   {4,50,4} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {50,2}*200
   4-fold quotients : {25,2}*100
   5-fold quotients : {10,4}*80
   10-fold quotients : {10,2}*40
   20-fold quotients : {5,2}*20
   25-fold quotients : {2,4}*16
   50-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {100,4}*800, {50,8}*800
   3-fold covers : {50,12}*1200, {150,4}*1200a
   4-fold covers : {200,4}*1600a, {100,4}*1600, {200,4}*1600b, {100,8}*1600a, {100,8}*1600b, {50,16}*1600
   5-fold covers : {250,4}*2000, {50,20}*2000a, {50,20}*2000b
Permutation Representation (GAP) :
s0 := (  2,  5)(  3,  4)(  6, 22)(  7, 21)(  8, 25)(  9, 24)( 10, 23)( 11, 17)
( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 27, 30)( 28, 29)( 31, 47)( 32, 46)
( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)( 40, 43)
( 52, 55)( 53, 54)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)( 61, 67)
( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 77, 80)( 78, 79)( 81, 97)( 82, 96)
( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)( 90, 93);;
s1 := (  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 22)( 12, 21)( 13, 25)
( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 31)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 42)( 43, 45)
( 51, 81)( 52, 85)( 53, 84)( 54, 83)( 55, 82)( 56, 76)( 57, 80)( 58, 79)
( 59, 78)( 60, 77)( 61, 97)( 62, 96)( 63,100)( 64, 99)( 65, 98)( 66, 92)
( 67, 91)( 68, 95)( 69, 94)( 70, 93)( 71, 87)( 72, 86)( 73, 90)( 74, 89)
( 75, 88);;
s2 := (  1, 51)(  2, 52)(  3, 53)(  4, 54)(  5, 55)(  6, 56)(  7, 57)(  8, 58)
(  9, 59)( 10, 60)( 11, 61)( 12, 62)( 13, 63)( 14, 64)( 15, 65)( 16, 66)
( 17, 67)( 18, 68)( 19, 69)( 20, 70)( 21, 71)( 22, 72)( 23, 73)( 24, 74)
( 25, 75)( 26, 76)( 27, 77)( 28, 78)( 29, 79)( 30, 80)( 31, 81)( 32, 82)
( 33, 83)( 34, 84)( 35, 85)( 36, 86)( 37, 87)( 38, 88)( 39, 89)( 40, 90)
( 41, 91)( 42, 92)( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)( 48, 98)
( 49, 99)( 50,100);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(100)!(  2,  5)(  3,  4)(  6, 22)(  7, 21)(  8, 25)(  9, 24)( 10, 23)
( 11, 17)( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 27, 30)( 28, 29)( 31, 47)
( 32, 46)( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)
( 40, 43)( 52, 55)( 53, 54)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)
( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 77, 80)( 78, 79)( 81, 97)
( 82, 96)( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)
( 90, 93);
s1 := Sym(100)!(  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 22)( 12, 21)
( 13, 25)( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 31)( 27, 35)( 28, 34)
( 29, 33)( 30, 32)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 42)
( 43, 45)( 51, 81)( 52, 85)( 53, 84)( 54, 83)( 55, 82)( 56, 76)( 57, 80)
( 58, 79)( 59, 78)( 60, 77)( 61, 97)( 62, 96)( 63,100)( 64, 99)( 65, 98)
( 66, 92)( 67, 91)( 68, 95)( 69, 94)( 70, 93)( 71, 87)( 72, 86)( 73, 90)
( 74, 89)( 75, 88);
s2 := Sym(100)!(  1, 51)(  2, 52)(  3, 53)(  4, 54)(  5, 55)(  6, 56)(  7, 57)
(  8, 58)(  9, 59)( 10, 60)( 11, 61)( 12, 62)( 13, 63)( 14, 64)( 15, 65)
( 16, 66)( 17, 67)( 18, 68)( 19, 69)( 20, 70)( 21, 71)( 22, 72)( 23, 73)
( 24, 74)( 25, 75)( 26, 76)( 27, 77)( 28, 78)( 29, 79)( 30, 80)( 31, 81)
( 32, 82)( 33, 83)( 34, 84)( 35, 85)( 36, 86)( 37, 87)( 38, 88)( 39, 89)
( 40, 90)( 41, 91)( 42, 92)( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)
( 48, 98)( 49, 99)( 50,100);
poly := sub<Sym(100)|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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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