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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,10,10}*2000b
if this polytope has a name.
Group : SmallGroup(2000,946)
Rank : 5
Schlafli Type : {2,5,10,10}
Number of vertices, edges, etc : 2, 5, 25, 50, 10
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 : {2,5,2,10}*400, {2,5,10,2}*400
   10-fold quotients : {2,5,2,5}*200
   25-fold quotients : {2,5,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope