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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,5,10}*2000
if this polytope has a name.
Group : SmallGroup(2000,946)
Rank : 5
Schlafli Type : {2,10,5,10}
Number of vertices, edges, etc : 2, 10, 25, 25, 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 : {2,2,5,10}*400, {2,10,5,2}*400
   25-fold quotients : {2,2,5,2}*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)( 28,104)( 29,103)( 30,107)( 31,106)
( 32,105)( 33,124)( 34,123)( 35,127)( 36,126)( 37,125)( 38,119)( 39,118)
( 40,122)( 41,121)( 42,120)( 43,114)( 44,113)( 45,117)( 46,116)( 47,115)
( 48,109)( 49,108)( 50,112)( 51,111)( 52,110)( 53, 79)( 54, 78)( 55, 82)
( 56, 81)( 57, 80)( 58, 99)( 59, 98)( 60,102)( 61,101)( 62,100)( 63, 94)
( 64, 93)( 65, 97)( 66, 96)( 67, 95)( 68, 89)( 69, 88)( 70, 92)( 71, 91)
( 72, 90)( 73, 84)( 74, 83)( 75, 87)( 76, 86)( 77, 85);;
s3 := (  3, 33)(  4, 37)(  5, 36)(  6, 35)(  7, 34)(  8, 28)(  9, 32)( 10, 31)
( 11, 30)( 12, 29)( 13, 48)( 14, 52)( 15, 51)( 16, 50)( 17, 49)( 18, 43)
( 19, 47)( 20, 46)( 21, 45)( 22, 44)( 23, 38)( 24, 42)( 25, 41)( 26, 40)
( 27, 39)( 53,108)( 54,112)( 55,111)( 56,110)( 57,109)( 58,103)( 59,107)
( 60,106)( 61,105)( 62,104)( 63,123)( 64,127)( 65,126)( 66,125)( 67,124)
( 68,118)( 69,122)( 70,121)( 71,120)( 72,119)( 73,113)( 74,117)( 75,116)
( 76,115)( 77,114)( 78, 83)( 79, 87)( 80, 86)( 81, 85)( 82, 84)( 88, 98)
( 89,102)( 90,101)( 91,100)( 92, 99)( 94, 97)( 95, 96);;
s4 := (  8, 23)(  9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 18)( 14, 19)( 15, 20)
( 16, 21)( 17, 22)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 43)
( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 58, 73)( 59, 74)( 60, 75)( 61, 76)
( 62, 77)( 63, 68)( 64, 69)( 65, 70)( 66, 71)( 67, 72)( 83, 98)( 84, 99)
( 85,100)( 86,101)( 87,102)( 88, 93)( 89, 94)( 90, 95)( 91, 96)( 92, 97)
(108,123)(109,124)(110,125)(111,126)(112,127)(113,118)(114,119)(115,120)
(116,121)(117,122);;
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, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)( 28,104)( 29,103)( 30,107)
( 31,106)( 32,105)( 33,124)( 34,123)( 35,127)( 36,126)( 37,125)( 38,119)
( 39,118)( 40,122)( 41,121)( 42,120)( 43,114)( 44,113)( 45,117)( 46,116)
( 47,115)( 48,109)( 49,108)( 50,112)( 51,111)( 52,110)( 53, 79)( 54, 78)
( 55, 82)( 56, 81)( 57, 80)( 58, 99)( 59, 98)( 60,102)( 61,101)( 62,100)
( 63, 94)( 64, 93)( 65, 97)( 66, 96)( 67, 95)( 68, 89)( 69, 88)( 70, 92)
( 71, 91)( 72, 90)( 73, 84)( 74, 83)( 75, 87)( 76, 86)( 77, 85);
s3 := Sym(127)!(  3, 33)(  4, 37)(  5, 36)(  6, 35)(  7, 34)(  8, 28)(  9, 32)
( 10, 31)( 11, 30)( 12, 29)( 13, 48)( 14, 52)( 15, 51)( 16, 50)( 17, 49)
( 18, 43)( 19, 47)( 20, 46)( 21, 45)( 22, 44)( 23, 38)( 24, 42)( 25, 41)
( 26, 40)( 27, 39)( 53,108)( 54,112)( 55,111)( 56,110)( 57,109)( 58,103)
( 59,107)( 60,106)( 61,105)( 62,104)( 63,123)( 64,127)( 65,126)( 66,125)
( 67,124)( 68,118)( 69,122)( 70,121)( 71,120)( 72,119)( 73,113)( 74,117)
( 75,116)( 76,115)( 77,114)( 78, 83)( 79, 87)( 80, 86)( 81, 85)( 82, 84)
( 88, 98)( 89,102)( 90,101)( 91,100)( 92, 99)( 94, 97)( 95, 96);
s4 := Sym(127)!(  8, 23)(  9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 18)( 14, 19)
( 15, 20)( 16, 21)( 17, 22)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)
( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 58, 73)( 59, 74)( 60, 75)
( 61, 76)( 62, 77)( 63, 68)( 64, 69)( 65, 70)( 66, 71)( 67, 72)( 83, 98)
( 84, 99)( 85,100)( 86,101)( 87,102)( 88, 93)( 89, 94)( 90, 95)( 91, 96)
( 92, 97)(108,123)(109,124)(110,125)(111,126)(112,127)(113,118)(114,119)
(115,120)(116,121)(117,122);
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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope