Polytope of Type {4,10,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10,4}*1600b
Also Known As : {{4,10}₄,{10,4|2}}. if this polytope has another name.
Group : SmallGroup(1600,10031)
Rank : 4
Schlafli Type : {4,10,4}
Number of vertices, edges, etc : 20, 100, 100, 4
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,10,2}*800
   4-fold quotients : {4,10,2}*400
   25-fold quotients : {4,2,4}*64
   50-fold quotients : {2,2,4}*32, {4,2,2}*32
   100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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