Polytope of Type {2,10,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,10}*2000d
if this polytope has a name.
Group : SmallGroup(2000,946)
Rank : 4
Schlafli Type : {2,10,10}
Number of vertices, edges, etc : 2, 50, 250, 50
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,10,10}*400a, {2,10,10}*400b, {2,10,10}*400c
   10-fold quotients : {2,5,10}*200, {2,10,5}*200
   25-fold quotients : {2,2,10}*80, {2,10,2}*80
   50-fold quotients : {2,2,5}*40, {2,5,2}*40
   125-fold quotients : {2,2,2}*16
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)( 28,109)( 29,108)( 30,112)( 31,111)
( 32,110)( 33,104)( 34,103)( 35,107)( 36,106)( 37,105)( 38,124)( 39,123)
( 40,127)( 41,126)( 42,125)( 43,119)( 44,118)( 45,122)( 46,121)( 47,120)
( 48,114)( 49,113)( 50,117)( 51,116)( 52,115)( 53, 84)( 54, 83)( 55, 87)
( 56, 86)( 57, 85)( 58, 79)( 59, 78)( 60, 82)( 61, 81)( 62, 80)( 63, 99)
( 64, 98)( 65,102)( 66,101)( 67,100)( 68, 94)( 69, 93)( 70, 97)( 71, 96)
( 72, 95)( 73, 89)( 74, 88)( 75, 92)( 76, 91)( 77, 90);;
s3 := (  3, 28)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 33)(  9, 37)( 10, 36)
( 11, 35)( 12, 34)( 13, 38)( 14, 42)( 15, 41)( 16, 40)( 17, 39)( 18, 43)
( 19, 47)( 20, 46)( 21, 45)( 22, 44)( 23, 48)( 24, 52)( 25, 51)( 26, 50)
( 27, 49)( 53,103)( 54,107)( 55,106)( 56,105)( 57,104)( 58,108)( 59,112)
( 60,111)( 61,110)( 62,109)( 63,113)( 64,117)( 65,116)( 66,115)( 67,114)
( 68,118)( 69,122)( 70,121)( 71,120)( 72,119)( 73,123)( 74,127)( 75,126)
( 76,125)( 77,124)( 79, 82)( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)
( 94, 97)( 95, 96)( 99,102)(100,101);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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)!(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)( 28,109)( 29,108)( 30,112)
( 31,111)( 32,110)( 33,104)( 34,103)( 35,107)( 36,106)( 37,105)( 38,124)
( 39,123)( 40,127)( 41,126)( 42,125)( 43,119)( 44,118)( 45,122)( 46,121)
( 47,120)( 48,114)( 49,113)( 50,117)( 51,116)( 52,115)( 53, 84)( 54, 83)
( 55, 87)( 56, 86)( 57, 85)( 58, 79)( 59, 78)( 60, 82)( 61, 81)( 62, 80)
( 63, 99)( 64, 98)( 65,102)( 66,101)( 67,100)( 68, 94)( 69, 93)( 70, 97)
( 71, 96)( 72, 95)( 73, 89)( 74, 88)( 75, 92)( 76, 91)( 77, 90);
s3 := Sym(127)!(  3, 28)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 33)(  9, 37)
( 10, 36)( 11, 35)( 12, 34)( 13, 38)( 14, 42)( 15, 41)( 16, 40)( 17, 39)
( 18, 43)( 19, 47)( 20, 46)( 21, 45)( 22, 44)( 23, 48)( 24, 52)( 25, 51)
( 26, 50)( 27, 49)( 53,103)( 54,107)( 55,106)( 56,105)( 57,104)( 58,108)
( 59,112)( 60,111)( 61,110)( 62,109)( 63,113)( 64,117)( 65,116)( 66,115)
( 67,114)( 68,118)( 69,122)( 70,121)( 71,120)( 72,119)( 73,123)( 74,127)
( 75,126)( 76,125)( 77,124)( 79, 82)( 80, 81)( 84, 87)( 85, 86)( 89, 92)
( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101);
poly := sub<Sym(127)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope