Polytope of Type {5,10,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,10,10,2}*2000b
if this polytope has a name.
Group : SmallGroup(2000,946)
Rank : 5
Schlafli Type : {5,10,10,2}
Number of vertices, edges, etc : 5, 25, 50, 10, 2
Order of s₀s₁s₂s₃s₄ : 10
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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) :
   5-fold quotients : {5,2,10,2}*400, {5,10,2,2}*400
   10-fold quotients : {5,2,5,2}*200
   25-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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)
( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)
( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)
( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)
(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)
(112,120)(113,119)(114,118)(115,117);;
s1 := (  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, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)( 63, 75)
( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 82)( 77, 81)( 78, 85)( 79, 84)
( 80, 83)( 86, 97)( 87, 96)( 88,100)( 89, 99)( 90, 98)( 91, 92)( 93, 95)
(101,107)(102,106)(103,110)(104,109)(105,108)(111,122)(112,121)(113,125)
(114,124)(115,123)(116,117)(118,120);;
s2 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31,106)
( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)( 39,113)
( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,121)( 47,125)
( 48,124)( 49,123)( 50,122)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)
( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)( 63, 89)
( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 96)
( 72,100)( 73, 99)( 74, 98)( 75, 97);;
s3 := (  1, 26)(  2, 27)(  3, 28)(  4, 29)(  5, 30)(  6, 31)(  7, 32)(  8, 33)
(  9, 34)( 10, 35)( 11, 36)( 12, 37)( 13, 38)( 14, 39)( 15, 40)( 16, 41)
( 17, 42)( 18, 43)( 19, 44)( 20, 45)( 21, 46)( 22, 47)( 23, 48)( 24, 49)
( 25, 50)( 51,101)( 52,102)( 53,103)( 54,104)( 55,105)( 56,106)( 57,107)
( 58,108)( 59,109)( 60,110)( 61,111)( 62,112)( 63,113)( 64,114)( 65,115)
( 66,116)( 67,117)( 68,118)( 69,119)( 70,120)( 71,121)( 72,122)( 73,123)
( 74,124)( 75,125);;
s4 := (126,127);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(127)!(  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)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)
( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)
( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)
( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)
(111,116)(112,120)(113,119)(114,118)(115,117);
s1 := Sym(127)!(  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, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)
( 63, 75)( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 82)( 77, 81)( 78, 85)
( 79, 84)( 80, 83)( 86, 97)( 87, 96)( 88,100)( 89, 99)( 90, 98)( 91, 92)
( 93, 95)(101,107)(102,106)(103,110)(104,109)(105,108)(111,122)(112,121)
(113,125)(114,124)(115,123)(116,117)(118,120);
s2 := Sym(127)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)
( 31,106)( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)
( 39,113)( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,121)
( 47,125)( 48,124)( 49,123)( 50,122)( 51, 76)( 52, 80)( 53, 79)( 54, 78)
( 55, 77)( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)
( 63, 89)( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)
( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97);
s3 := Sym(127)!(  1, 26)(  2, 27)(  3, 28)(  4, 29)(  5, 30)(  6, 31)(  7, 32)
(  8, 33)(  9, 34)( 10, 35)( 11, 36)( 12, 37)( 13, 38)( 14, 39)( 15, 40)
( 16, 41)( 17, 42)( 18, 43)( 19, 44)( 20, 45)( 21, 46)( 22, 47)( 23, 48)
( 24, 49)( 25, 50)( 51,101)( 52,102)( 53,103)( 54,104)( 55,105)( 56,106)
( 57,107)( 58,108)( 59,109)( 60,110)( 61,111)( 62,112)( 63,113)( 64,114)
( 65,115)( 66,116)( 67,117)( 68,118)( 69,119)( 70,120)( 71,121)( 72,122)
( 73,123)( 74,124)( 75,125);
s4 := Sym(127)!(126,127);
poly := sub<Sym(127)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope