Polytope of Type {2,30,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,10}*1200c
if this polytope has a name.
Group : SmallGroup(1200,1028)
Rank : 4
Schlafli Type : {2,30,10}
Number of vertices, edges, etc : 2, 30, 150, 10
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) :
   2-fold quotients : {2,15,10}*600
   3-fold quotients : {2,10,10}*400c
   5-fold quotients : {2,30,2}*240
   6-fold quotients : {2,5,10}*200
   10-fold quotients : {2,15,2}*120
   15-fold quotients : {2,10,2}*80
   25-fold quotients : {2,6,2}*48
   30-fold quotients : {2,5,2}*40
   50-fold quotients : {2,3,2}*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)( 28, 53)( 29, 57)( 30, 56)( 31, 55)
( 32, 54)( 33, 73)( 34, 77)( 35, 76)( 36, 75)( 37, 74)( 38, 68)( 39, 72)
( 40, 71)( 41, 70)( 42, 69)( 43, 63)( 44, 67)( 45, 66)( 46, 65)( 47, 64)
( 48, 58)( 49, 62)( 50, 61)( 51, 60)( 52, 59)( 79, 82)( 80, 81)( 83, 98)
( 84,102)( 85,101)( 86,100)( 87, 99)( 88, 93)( 89, 97)( 90, 96)( 91, 95)
( 92, 94)(103,128)(104,132)(105,131)(106,130)(107,129)(108,148)(109,152)
(110,151)(111,150)(112,149)(113,143)(114,147)(115,146)(116,145)(117,144)
(118,138)(119,142)(120,141)(121,140)(122,139)(123,133)(124,137)(125,136)
(126,135)(127,134);;
s2 := (  3,109)(  4,108)(  5,112)(  6,111)(  7,110)(  8,104)(  9,103)( 10,107)
( 11,106)( 12,105)( 13,124)( 14,123)( 15,127)( 16,126)( 17,125)( 18,119)
( 19,118)( 20,122)( 21,121)( 22,120)( 23,114)( 24,113)( 25,117)( 26,116)
( 27,115)( 28, 84)( 29, 83)( 30, 87)( 31, 86)( 32, 85)( 33, 79)( 34, 78)
( 35, 82)( 36, 81)( 37, 80)( 38, 99)( 39, 98)( 40,102)( 41,101)( 42,100)
( 43, 94)( 44, 93)( 45, 97)( 46, 96)( 47, 95)( 48, 89)( 49, 88)( 50, 92)
( 51, 91)( 52, 90)( 53,134)( 54,133)( 55,137)( 56,136)( 57,135)( 58,129)
( 59,128)( 60,132)( 61,131)( 62,130)( 63,149)( 64,148)( 65,152)( 66,151)
( 67,150)( 68,144)( 69,143)( 70,147)( 71,146)( 72,145)( 73,139)( 74,138)
( 75,142)( 76,141)( 77,140);;
s3 := (  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);;
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*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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)( 28, 53)( 29, 57)( 30, 56)
( 31, 55)( 32, 54)( 33, 73)( 34, 77)( 35, 76)( 36, 75)( 37, 74)( 38, 68)
( 39, 72)( 40, 71)( 41, 70)( 42, 69)( 43, 63)( 44, 67)( 45, 66)( 46, 65)
( 47, 64)( 48, 58)( 49, 62)( 50, 61)( 51, 60)( 52, 59)( 79, 82)( 80, 81)
( 83, 98)( 84,102)( 85,101)( 86,100)( 87, 99)( 88, 93)( 89, 97)( 90, 96)
( 91, 95)( 92, 94)(103,128)(104,132)(105,131)(106,130)(107,129)(108,148)
(109,152)(110,151)(111,150)(112,149)(113,143)(114,147)(115,146)(116,145)
(117,144)(118,138)(119,142)(120,141)(121,140)(122,139)(123,133)(124,137)
(125,136)(126,135)(127,134);
s2 := Sym(152)!(  3,109)(  4,108)(  5,112)(  6,111)(  7,110)(  8,104)(  9,103)
( 10,107)( 11,106)( 12,105)( 13,124)( 14,123)( 15,127)( 16,126)( 17,125)
( 18,119)( 19,118)( 20,122)( 21,121)( 22,120)( 23,114)( 24,113)( 25,117)
( 26,116)( 27,115)( 28, 84)( 29, 83)( 30, 87)( 31, 86)( 32, 85)( 33, 79)
( 34, 78)( 35, 82)( 36, 81)( 37, 80)( 38, 99)( 39, 98)( 40,102)( 41,101)
( 42,100)( 43, 94)( 44, 93)( 45, 97)( 46, 96)( 47, 95)( 48, 89)( 49, 88)
( 50, 92)( 51, 91)( 52, 90)( 53,134)( 54,133)( 55,137)( 56,136)( 57,135)
( 58,129)( 59,128)( 60,132)( 61,131)( 62,130)( 63,149)( 64,148)( 65,152)
( 66,151)( 67,150)( 68,144)( 69,143)( 70,147)( 71,146)( 72,145)( 73,139)
( 74,138)( 75,142)( 76,141)( 77,140);
s3 := 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);
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope