Polytope of Type {20,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,10,2}*800b
if this polytope has a name.
Group : SmallGroup(800,1127)
Rank : 4
Schlafli Type : {20,10,2}
Number of vertices, edges, etc : 20, 100, 10, 2
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,10,2,2} of size 1600
Vertex Figure Of :
   {2,20,10,2} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,10,2}*400c
   4-fold quotients : {5,10,2}*200
   5-fold quotients : {20,2,2}*160
   10-fold quotients : {10,2,2}*80
   20-fold quotients : {5,2,2}*40
   25-fold quotients : {4,2,2}*32
   50-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {40,10,2}*1600b, {20,20,2}*1600c, {20,10,4}*1600b
Permutation Representation (GAP) :

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

to this polytope