Polytope of Type {10,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,30}*600c
if this polytope has a name.
Group : SmallGroup(600,195)
Rank : 3
Schlafli Type : {10,30}
Number of vertices, edges, etc : 10, 150, 30
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,30,2} of size 1200
Vertex Figure Of :
   {2,10,30} of size 1200
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,15}*300
   3-fold quotients : {10,10}*200b
   5-fold quotients : {2,30}*120
   6-fold quotients : {10,5}*100
   10-fold quotients : {2,15}*60
   15-fold quotients : {2,10}*40
   25-fold quotients : {2,6}*24
   30-fold quotients : {2,5}*20
   50-fold quotients : {2,3}*12
   75-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,60}*1200c, {20,30}*1200c
   3-fold covers : {10,90}*1800c, {30,30}*1800d, {30,30}*1800h
Permutation Representation (GAP) :

s0 := (  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)( 59, 74)
( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)
( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)
(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)
(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)
(137,142)(138,143)(139,144)(140,145);;
s1 := (  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 21)( 12, 25)( 13, 24)
( 14, 23)( 15, 22)( 17, 20)( 18, 19)( 26, 56)( 27, 60)( 28, 59)( 29, 58)
( 30, 57)( 31, 51)( 32, 55)( 33, 54)( 34, 53)( 35, 52)( 36, 71)( 37, 75)
( 38, 74)( 39, 73)( 40, 72)( 41, 66)( 42, 70)( 43, 69)( 44, 68)( 45, 67)
( 46, 61)( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 76, 81)( 77, 85)( 78, 84)
( 79, 83)( 80, 82)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 92, 95)
( 93, 94)(101,131)(102,135)(103,134)(104,133)(105,132)(106,126)(107,130)
(108,129)(109,128)(110,127)(111,146)(112,150)(113,149)(114,148)(115,147)
(116,141)(117,145)(118,144)(119,143)(120,142)(121,136)(122,140)(123,139)
(124,138)(125,137);;
s2 := (  1,102)(  2,101)(  3,105)(  4,104)(  5,103)(  6,122)(  7,121)(  8,125)
(  9,124)( 10,123)( 11,117)( 12,116)( 13,120)( 14,119)( 15,118)( 16,112)
( 17,111)( 18,115)( 19,114)( 20,113)( 21,107)( 22,106)( 23,110)( 24,109)
( 25,108)( 26, 77)( 27, 76)( 28, 80)( 29, 79)( 30, 78)( 31, 97)( 32, 96)
( 33,100)( 34, 99)( 35, 98)( 36, 92)( 37, 91)( 38, 95)( 39, 94)( 40, 93)
( 41, 87)( 42, 86)( 43, 90)( 44, 89)( 45, 88)( 46, 82)( 47, 81)( 48, 85)
( 49, 84)( 50, 83)( 51,127)( 52,126)( 53,130)( 54,129)( 55,128)( 56,147)
( 57,146)( 58,150)( 59,149)( 60,148)( 61,142)( 62,141)( 63,145)( 64,144)
( 65,143)( 66,137)( 67,136)( 68,140)( 69,139)( 70,138)( 71,132)( 72,131)
( 73,135)( 74,134)( 75,133);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(150)!(  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)
( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)
( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)
( 90, 95)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)
(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)
(136,141)(137,142)(138,143)(139,144)(140,145);
s1 := Sym(150)!(  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 21)( 12, 25)
( 13, 24)( 14, 23)( 15, 22)( 17, 20)( 18, 19)( 26, 56)( 27, 60)( 28, 59)
( 29, 58)( 30, 57)( 31, 51)( 32, 55)( 33, 54)( 34, 53)( 35, 52)( 36, 71)
( 37, 75)( 38, 74)( 39, 73)( 40, 72)( 41, 66)( 42, 70)( 43, 69)( 44, 68)
( 45, 67)( 46, 61)( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 76, 81)( 77, 85)
( 78, 84)( 79, 83)( 80, 82)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)
( 92, 95)( 93, 94)(101,131)(102,135)(103,134)(104,133)(105,132)(106,126)
(107,130)(108,129)(109,128)(110,127)(111,146)(112,150)(113,149)(114,148)
(115,147)(116,141)(117,145)(118,144)(119,143)(120,142)(121,136)(122,140)
(123,139)(124,138)(125,137);
s2 := Sym(150)!(  1,102)(  2,101)(  3,105)(  4,104)(  5,103)(  6,122)(  7,121)
(  8,125)(  9,124)( 10,123)( 11,117)( 12,116)( 13,120)( 14,119)( 15,118)
( 16,112)( 17,111)( 18,115)( 19,114)( 20,113)( 21,107)( 22,106)( 23,110)
( 24,109)( 25,108)( 26, 77)( 27, 76)( 28, 80)( 29, 79)( 30, 78)( 31, 97)
( 32, 96)( 33,100)( 34, 99)( 35, 98)( 36, 92)( 37, 91)( 38, 95)( 39, 94)
( 40, 93)( 41, 87)( 42, 86)( 43, 90)( 44, 89)( 45, 88)( 46, 82)( 47, 81)
( 48, 85)( 49, 84)( 50, 83)( 51,127)( 52,126)( 53,130)( 54,129)( 55,128)
( 56,147)( 57,146)( 58,150)( 59,149)( 60,148)( 61,142)( 62,141)( 63,145)
( 64,144)( 65,143)( 66,137)( 67,136)( 68,140)( 69,139)( 70,138)( 71,132)
( 72,131)( 73,135)( 74,134)( 75,133);
poly := sub<Sym(150)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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 >;

References : None.
to this polytope