Polytope of Type {14,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,22}*616
Also Known As : {14,22|2}. if this polytope has another name.
Group : SmallGroup(616,31)
Rank : 3
Schlafli Type : {14,22}
Number of vertices, edges, etc : 14, 154, 22
Order of s₀s₁s₂ : 154
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {14,22,2} of size 1232
Vertex Figure Of :
   {2,14,22} of size 1232
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {2,22}*88
   11-fold quotients : {14,2}*56
   14-fold quotients : {2,11}*44
   22-fold quotients : {7,2}*28
   77-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {28,22}*1232, {14,44}*1232
   3-fold covers : {42,22}*1848, {14,66}*1848
Permutation Representation (GAP) :

s0 := ( 12, 67)( 13, 68)( 14, 69)( 15, 70)( 16, 71)( 17, 72)( 18, 73)( 19, 74)
( 20, 75)( 21, 76)( 22, 77)( 23, 56)( 24, 57)( 25, 58)( 26, 59)( 27, 60)
( 28, 61)( 29, 62)( 30, 63)( 31, 64)( 32, 65)( 33, 66)( 34, 45)( 35, 46)
( 36, 47)( 37, 48)( 38, 49)( 39, 50)( 40, 51)( 41, 52)( 42, 53)( 43, 54)
( 44, 55)( 89,144)( 90,145)( 91,146)( 92,147)( 93,148)( 94,149)( 95,150)
( 96,151)( 97,152)( 98,153)( 99,154)(100,133)(101,134)(102,135)(103,136)
(104,137)(105,138)(106,139)(107,140)(108,141)(109,142)(110,143)(111,122)
(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)(118,129)(119,130)
(120,131)(121,132);;
s1 := (  1, 12)(  2, 22)(  3, 21)(  4, 20)(  5, 19)(  6, 18)(  7, 17)(  8, 16)
(  9, 15)( 10, 14)( 11, 13)( 23, 67)( 24, 77)( 25, 76)( 26, 75)( 27, 74)
( 28, 73)( 29, 72)( 30, 71)( 31, 70)( 32, 69)( 33, 68)( 34, 56)( 35, 66)
( 36, 65)( 37, 64)( 38, 63)( 39, 62)( 40, 61)( 41, 60)( 42, 59)( 43, 58)
( 44, 57)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 78, 89)( 79, 99)
( 80, 98)( 81, 97)( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)
( 88, 90)(100,144)(101,154)(102,153)(103,152)(104,151)(105,150)(106,149)
(107,148)(108,147)(109,146)(110,145)(111,133)(112,143)(113,142)(114,141)
(115,140)(116,139)(117,138)(118,137)(119,136)(120,135)(121,134)(123,132)
(124,131)(125,130)(126,129)(127,128);;
s2 := (  1, 79)(  2, 78)(  3, 88)(  4, 87)(  5, 86)(  6, 85)(  7, 84)(  8, 83)
(  9, 82)( 10, 81)( 11, 80)( 12, 90)( 13, 89)( 14, 99)( 15, 98)( 16, 97)
( 17, 96)( 18, 95)( 19, 94)( 20, 93)( 21, 92)( 22, 91)( 23,101)( 24,100)
( 25,110)( 26,109)( 27,108)( 28,107)( 29,106)( 30,105)( 31,104)( 32,103)
( 33,102)( 34,112)( 35,111)( 36,121)( 37,120)( 38,119)( 39,118)( 40,117)
( 41,116)( 42,115)( 43,114)( 44,113)( 45,123)( 46,122)( 47,132)( 48,131)
( 49,130)( 50,129)( 51,128)( 52,127)( 53,126)( 54,125)( 55,124)( 56,134)
( 57,133)( 58,143)( 59,142)( 60,141)( 61,140)( 62,139)( 63,138)( 64,137)
( 65,136)( 66,135)( 67,145)( 68,144)( 69,154)( 70,153)( 71,152)( 72,151)
( 73,150)( 74,149)( 75,148)( 76,147)( 77,146);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(154)!( 12, 67)( 13, 68)( 14, 69)( 15, 70)( 16, 71)( 17, 72)( 18, 73)
( 19, 74)( 20, 75)( 21, 76)( 22, 77)( 23, 56)( 24, 57)( 25, 58)( 26, 59)
( 27, 60)( 28, 61)( 29, 62)( 30, 63)( 31, 64)( 32, 65)( 33, 66)( 34, 45)
( 35, 46)( 36, 47)( 37, 48)( 38, 49)( 39, 50)( 40, 51)( 41, 52)( 42, 53)
( 43, 54)( 44, 55)( 89,144)( 90,145)( 91,146)( 92,147)( 93,148)( 94,149)
( 95,150)( 96,151)( 97,152)( 98,153)( 99,154)(100,133)(101,134)(102,135)
(103,136)(104,137)(105,138)(106,139)(107,140)(108,141)(109,142)(110,143)
(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)(118,129)
(119,130)(120,131)(121,132);
s1 := Sym(154)!(  1, 12)(  2, 22)(  3, 21)(  4, 20)(  5, 19)(  6, 18)(  7, 17)
(  8, 16)(  9, 15)( 10, 14)( 11, 13)( 23, 67)( 24, 77)( 25, 76)( 26, 75)
( 27, 74)( 28, 73)( 29, 72)( 30, 71)( 31, 70)( 32, 69)( 33, 68)( 34, 56)
( 35, 66)( 36, 65)( 37, 64)( 38, 63)( 39, 62)( 40, 61)( 41, 60)( 42, 59)
( 43, 58)( 44, 57)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 78, 89)
( 79, 99)( 80, 98)( 81, 97)( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)
( 87, 91)( 88, 90)(100,144)(101,154)(102,153)(103,152)(104,151)(105,150)
(106,149)(107,148)(108,147)(109,146)(110,145)(111,133)(112,143)(113,142)
(114,141)(115,140)(116,139)(117,138)(118,137)(119,136)(120,135)(121,134)
(123,132)(124,131)(125,130)(126,129)(127,128);
s2 := Sym(154)!(  1, 79)(  2, 78)(  3, 88)(  4, 87)(  5, 86)(  6, 85)(  7, 84)
(  8, 83)(  9, 82)( 10, 81)( 11, 80)( 12, 90)( 13, 89)( 14, 99)( 15, 98)
( 16, 97)( 17, 96)( 18, 95)( 19, 94)( 20, 93)( 21, 92)( 22, 91)( 23,101)
( 24,100)( 25,110)( 26,109)( 27,108)( 28,107)( 29,106)( 30,105)( 31,104)
( 32,103)( 33,102)( 34,112)( 35,111)( 36,121)( 37,120)( 38,119)( 39,118)
( 40,117)( 41,116)( 42,115)( 43,114)( 44,113)( 45,123)( 46,122)( 47,132)
( 48,131)( 49,130)( 50,129)( 51,128)( 52,127)( 53,126)( 54,125)( 55,124)
( 56,134)( 57,133)( 58,143)( 59,142)( 60,141)( 61,140)( 62,139)( 63,138)
( 64,137)( 65,136)( 66,135)( 67,145)( 68,144)( 69,154)( 70,153)( 71,152)
( 72,151)( 73,150)( 74,149)( 75,148)( 76,147)( 77,146);
poly := sub<Sym(154)|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, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*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 >;

References : None.
to this polytope