Polytope of Type {2,10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,6}*1200b
if this polytope has a name.
Group : SmallGroup(1200,980)
Rank : 4
Schlafli Type : {2,10,6}
Number of vertices, edges, etc : 2, 50, 150, 30
Order of s₀s₁s₂s₃ : 6
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) :
   2-fold quotients : {2,10,3}*600
   25-fold quotients : {2,2,6}*48
   50-fold quotients : {2,2,3}*24
   75-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)(129,132)(130,131)(133,148)(134,152)
(135,151)(136,150)(137,149)(138,143)(139,147)(140,146)(141,145)(142,144);;
s2 := (  3,  8)(  4, 14)(  5, 20)(  6, 26)( 10, 15)( 11, 21)( 12, 27)( 13, 23)
( 17, 22)( 19, 24)( 28, 58)( 29, 64)( 30, 70)( 31, 76)( 32, 57)( 33, 53)
( 34, 59)( 35, 65)( 36, 71)( 37, 77)( 38, 73)( 39, 54)( 40, 60)( 41, 66)
( 42, 72)( 43, 68)( 44, 74)( 45, 55)( 46, 61)( 47, 67)( 48, 63)( 49, 69)
( 50, 75)( 51, 56)( 52, 62)( 78, 83)( 79, 89)( 80, 95)( 81,101)( 85, 90)
( 86, 96)( 87,102)( 88, 98)( 92, 97)( 94, 99)(103,133)(104,139)(105,145)
(106,151)(107,132)(108,128)(109,134)(110,140)(111,146)(112,152)(113,148)
(114,129)(115,135)(116,141)(117,147)(118,143)(119,149)(120,130)(121,136)
(122,142)(123,138)(124,144)(125,150)(126,131)(127,137);;
s3 := (  3,103)(  4,126)(  5,119)(  6,117)(  7,110)(  8,116)(  9,109)( 10,107)
( 11,125)( 12,118)( 13,124)( 14,122)( 15,115)( 16,108)( 17,106)( 18,112)
( 19,105)( 20,123)( 21,121)( 22,114)( 23,120)( 24,113)( 25,111)( 26,104)
( 27,127)( 28, 78)( 29,101)( 30, 94)( 31, 92)( 32, 85)( 33, 91)( 34, 84)
( 35, 82)( 36,100)( 37, 93)( 38, 99)( 39, 97)( 40, 90)( 41, 83)( 42, 81)
( 43, 87)( 44, 80)( 45, 98)( 46, 96)( 47, 89)( 48, 95)( 49, 88)( 50, 86)
( 51, 79)( 52,102)( 53,128)( 54,151)( 55,144)( 56,142)( 57,135)( 58,141)
( 59,134)( 60,132)( 61,150)( 62,143)( 63,149)( 64,147)( 65,140)( 66,133)
( 67,131)( 68,137)( 69,130)( 70,148)( 71,146)( 72,139)( 73,145)( 74,138)
( 75,136)( 76,129)( 77,152);;
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, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2, 
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(152)!(1,2);
s1 := Sym(152)!(  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)(129,132)(130,131)(133,148)
(134,152)(135,151)(136,150)(137,149)(138,143)(139,147)(140,146)(141,145)
(142,144);
s2 := Sym(152)!(  3,  8)(  4, 14)(  5, 20)(  6, 26)( 10, 15)( 11, 21)( 12, 27)
( 13, 23)( 17, 22)( 19, 24)( 28, 58)( 29, 64)( 30, 70)( 31, 76)( 32, 57)
( 33, 53)( 34, 59)( 35, 65)( 36, 71)( 37, 77)( 38, 73)( 39, 54)( 40, 60)
( 41, 66)( 42, 72)( 43, 68)( 44, 74)( 45, 55)( 46, 61)( 47, 67)( 48, 63)
( 49, 69)( 50, 75)( 51, 56)( 52, 62)( 78, 83)( 79, 89)( 80, 95)( 81,101)
( 85, 90)( 86, 96)( 87,102)( 88, 98)( 92, 97)( 94, 99)(103,133)(104,139)
(105,145)(106,151)(107,132)(108,128)(109,134)(110,140)(111,146)(112,152)
(113,148)(114,129)(115,135)(116,141)(117,147)(118,143)(119,149)(120,130)
(121,136)(122,142)(123,138)(124,144)(125,150)(126,131)(127,137);
s3 := Sym(152)!(  3,103)(  4,126)(  5,119)(  6,117)(  7,110)(  8,116)(  9,109)
( 10,107)( 11,125)( 12,118)( 13,124)( 14,122)( 15,115)( 16,108)( 17,106)
( 18,112)( 19,105)( 20,123)( 21,121)( 22,114)( 23,120)( 24,113)( 25,111)
( 26,104)( 27,127)( 28, 78)( 29,101)( 30, 94)( 31, 92)( 32, 85)( 33, 91)
( 34, 84)( 35, 82)( 36,100)( 37, 93)( 38, 99)( 39, 97)( 40, 90)( 41, 83)
( 42, 81)( 43, 87)( 44, 80)( 45, 98)( 46, 96)( 47, 89)( 48, 95)( 49, 88)
( 50, 86)( 51, 79)( 52,102)( 53,128)( 54,151)( 55,144)( 56,142)( 57,135)
( 58,141)( 59,134)( 60,132)( 61,150)( 62,143)( 63,149)( 64,147)( 65,140)
( 66,133)( 67,131)( 68,137)( 69,130)( 70,148)( 71,146)( 72,139)( 73,145)
( 74,138)( 75,136)( 76,129)( 77,152);
poly := sub<Sym(152)|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, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope