Polytope of Type {10,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10,2}*400c
if this polytope has a name.
Group : SmallGroup(400,218)
Rank : 4
Schlafli Type : {10,10,2}
Number of vertices, edges, etc : 10, 50, 10, 2
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,10,2,2} of size 800
   {10,10,2,3} of size 1200
   {10,10,2,4} of size 1600
   {10,10,2,5} of size 2000
Vertex Figure Of :
   {2,10,10,2} of size 800
   {4,10,10,2} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,10,2}*200
   5-fold quotients : {10,2,2}*80
   10-fold quotients : {5,2,2}*40
   25-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,10,2}*800b, {10,10,4}*800c, {10,20,2}*800c
   3-fold covers : {10,10,6}*1200c, {10,30,2}*1200a, {30,10,2}*1200c
   4-fold covers : {40,10,2}*1600b, {20,20,2}*1600c, {20,10,4}*1600b, {10,10,8}*1600c, {10,40,2}*1600c, {10,20,4}*1600c
   5-fold covers : {50,10,2}*2000b, {10,10,2}*2000a, {10,10,10}*2000g, {10,10,2}*2000d
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope