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

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

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

to this polytope