Polytope of Type {2,150}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,150}*600
if this polytope has a name.
Group : SmallGroup(600,43)
Rank : 3
Schlafli Type : {2,150}
Number of vertices, edges, etc : 2, 150, 150
Order of s₀s₁s₂ : 150
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,150,2} of size 1200
Vertex Figure Of :
   {2,2,150} of size 1200
   {3,2,150} of size 1800
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,75}*300
   3-fold quotients : {2,50}*200
   5-fold quotients : {2,30}*120
   6-fold quotients : {2,25}*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 : {2,300}*1200, {4,150}*1200a
   3-fold covers : {2,450}*1800, {6,150}*1800b, {6,150}*1800c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  8, 24)(  9, 23)( 10, 27)( 11, 26)( 12, 25)( 13, 19)
( 14, 18)( 15, 22)( 16, 21)( 17, 20)( 28, 53)( 29, 57)( 30, 56)( 31, 55)
( 32, 54)( 33, 74)( 34, 73)( 35, 77)( 36, 76)( 37, 75)( 38, 69)( 39, 68)
( 40, 72)( 41, 71)( 42, 70)( 43, 64)( 44, 63)( 45, 67)( 46, 66)( 47, 65)
( 48, 59)( 49, 58)( 50, 62)( 51, 61)( 52, 60)( 79, 82)( 80, 81)( 83, 99)
( 84, 98)( 85,102)( 86,101)( 87,100)( 88, 94)( 89, 93)( 90, 97)( 91, 96)
( 92, 95)(103,128)(104,132)(105,131)(106,130)(107,129)(108,149)(109,148)
(110,152)(111,151)(112,150)(113,144)(114,143)(115,147)(116,146)(117,145)
(118,139)(119,138)(120,142)(121,141)(122,140)(123,134)(124,133)(125,137)
(126,136)(127,135);;
s2 := (  3,108)(  4,112)(  5,111)(  6,110)(  7,109)(  8,103)(  9,107)( 10,106)
( 11,105)( 12,104)( 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, 83)( 29, 87)( 30, 86)( 31, 85)( 32, 84)( 33, 78)( 34, 82)
( 35, 81)( 36, 80)( 37, 79)( 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)( 53,133)( 54,137)( 55,136)( 56,135)( 57,134)( 58,128)
( 59,132)( 60,131)( 61,130)( 62,129)( 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);;
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*s1*s0*s1, s0*s2*s0*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*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*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*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*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, 24)(  9, 23)( 10, 27)( 11, 26)( 12, 25)
( 13, 19)( 14, 18)( 15, 22)( 16, 21)( 17, 20)( 28, 53)( 29, 57)( 30, 56)
( 31, 55)( 32, 54)( 33, 74)( 34, 73)( 35, 77)( 36, 76)( 37, 75)( 38, 69)
( 39, 68)( 40, 72)( 41, 71)( 42, 70)( 43, 64)( 44, 63)( 45, 67)( 46, 66)
( 47, 65)( 48, 59)( 49, 58)( 50, 62)( 51, 61)( 52, 60)( 79, 82)( 80, 81)
( 83, 99)( 84, 98)( 85,102)( 86,101)( 87,100)( 88, 94)( 89, 93)( 90, 97)
( 91, 96)( 92, 95)(103,128)(104,132)(105,131)(106,130)(107,129)(108,149)
(109,148)(110,152)(111,151)(112,150)(113,144)(114,143)(115,147)(116,146)
(117,145)(118,139)(119,138)(120,142)(121,141)(122,140)(123,134)(124,133)
(125,137)(126,136)(127,135);
s2 := Sym(152)!(  3,108)(  4,112)(  5,111)(  6,110)(  7,109)(  8,103)(  9,107)
( 10,106)( 11,105)( 12,104)( 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, 83)( 29, 87)( 30, 86)( 31, 85)( 32, 84)( 33, 78)
( 34, 82)( 35, 81)( 36, 80)( 37, 79)( 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)( 53,133)( 54,137)( 55,136)( 56,135)( 57,134)
( 58,128)( 59,132)( 60,131)( 61,130)( 62,129)( 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);
poly := sub<Sym(152)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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