Polytope of Type {2,10,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,30}*1200b
if this polytope has a name.
Group : SmallGroup(1200,1028)
Rank : 4
Schlafli Type : {2,10,30}
Number of vertices, edges, etc : 2, 10, 150, 30
Order of s₀s₁s₂s₃ : 30
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) :
   3-fold quotients : {2,10,10}*400a
   5-fold quotients : {2,10,6}*240, {2,2,30}*240
   10-fold quotients : {2,2,15}*120
   15-fold quotients : {2,2,10}*80, {2,10,2}*80
   25-fold quotients : {2,2,6}*48
   30-fold quotients : {2,2,5}*40, {2,5,2}*40
   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 := (  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)(133,148)(134,149)(135,150)(136,151)(137,152)(138,143)
(139,144)(140,145)(141,146)(142,147);;
s2 := (  3,  8)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 13, 23)( 14, 27)( 15, 26)
( 16, 25)( 17, 24)( 19, 22)( 20, 21)( 28, 58)( 29, 62)( 30, 61)( 31, 60)
( 32, 59)( 33, 53)( 34, 57)( 35, 56)( 36, 55)( 37, 54)( 38, 73)( 39, 77)
( 40, 76)( 41, 75)( 42, 74)( 43, 68)( 44, 72)( 45, 71)( 46, 70)( 47, 69)
( 48, 63)( 49, 67)( 50, 66)( 51, 65)( 52, 64)( 78, 83)( 79, 87)( 80, 86)
( 81, 85)( 82, 84)( 88, 98)( 89,102)( 90,101)( 91,100)( 92, 99)( 94, 97)
( 95, 96)(103,133)(104,137)(105,136)(106,135)(107,134)(108,128)(109,132)
(110,131)(111,130)(112,129)(113,148)(114,152)(115,151)(116,150)(117,149)
(118,143)(119,147)(120,146)(121,145)(122,144)(123,138)(124,142)(125,141)
(126,140)(127,139);;
s3 := (  3,104)(  4,103)(  5,107)(  6,106)(  7,105)(  8,109)(  9,108)( 10,112)
( 11,111)( 12,110)( 13,114)( 14,113)( 15,117)( 16,116)( 17,115)( 18,119)
( 19,118)( 20,122)( 21,121)( 22,120)( 23,124)( 24,123)( 25,127)( 26,126)
( 27,125)( 28, 79)( 29, 78)( 30, 82)( 31, 81)( 32, 80)( 33, 84)( 34, 83)
( 35, 87)( 36, 86)( 37, 85)( 38, 89)( 39, 88)( 40, 92)( 41, 91)( 42, 90)
( 43, 94)( 44, 93)( 45, 97)( 46, 96)( 47, 95)( 48, 99)( 49, 98)( 50,102)
( 51,101)( 52,100)( 53,129)( 54,128)( 55,132)( 56,131)( 57,130)( 58,134)
( 59,133)( 60,137)( 61,136)( 62,135)( 63,139)( 64,138)( 65,142)( 66,141)
( 67,140)( 68,144)( 69,143)( 70,147)( 71,146)( 72,145)( 73,149)( 74,148)
( 75,152)( 76,151)( 77,150);;
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*s1*s2*s3*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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(152)!(1,2);
s1 := Sym(152)!(  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)(133,148)(134,149)(135,150)(136,151)(137,152)
(138,143)(139,144)(140,145)(141,146)(142,147);
s2 := Sym(152)!(  3,  8)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 13, 23)( 14, 27)
( 15, 26)( 16, 25)( 17, 24)( 19, 22)( 20, 21)( 28, 58)( 29, 62)( 30, 61)
( 31, 60)( 32, 59)( 33, 53)( 34, 57)( 35, 56)( 36, 55)( 37, 54)( 38, 73)
( 39, 77)( 40, 76)( 41, 75)( 42, 74)( 43, 68)( 44, 72)( 45, 71)( 46, 70)
( 47, 69)( 48, 63)( 49, 67)( 50, 66)( 51, 65)( 52, 64)( 78, 83)( 79, 87)
( 80, 86)( 81, 85)( 82, 84)( 88, 98)( 89,102)( 90,101)( 91,100)( 92, 99)
( 94, 97)( 95, 96)(103,133)(104,137)(105,136)(106,135)(107,134)(108,128)
(109,132)(110,131)(111,130)(112,129)(113,148)(114,152)(115,151)(116,150)
(117,149)(118,143)(119,147)(120,146)(121,145)(122,144)(123,138)(124,142)
(125,141)(126,140)(127,139);
s3 := Sym(152)!(  3,104)(  4,103)(  5,107)(  6,106)(  7,105)(  8,109)(  9,108)
( 10,112)( 11,111)( 12,110)( 13,114)( 14,113)( 15,117)( 16,116)( 17,115)
( 18,119)( 19,118)( 20,122)( 21,121)( 22,120)( 23,124)( 24,123)( 25,127)
( 26,126)( 27,125)( 28, 79)( 29, 78)( 30, 82)( 31, 81)( 32, 80)( 33, 84)
( 34, 83)( 35, 87)( 36, 86)( 37, 85)( 38, 89)( 39, 88)( 40, 92)( 41, 91)
( 42, 90)( 43, 94)( 44, 93)( 45, 97)( 46, 96)( 47, 95)( 48, 99)( 49, 98)
( 50,102)( 51,101)( 52,100)( 53,129)( 54,128)( 55,132)( 56,131)( 57,130)
( 58,134)( 59,133)( 60,137)( 61,136)( 62,135)( 63,139)( 64,138)( 65,142)
( 66,141)( 67,140)( 68,144)( 69,143)( 70,147)( 71,146)( 72,145)( 73,149)
( 74,148)( 75,152)( 76,151)( 77,150);
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*s1*s2*s3*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope