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Polytope of Type {2,30,10}

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

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