# Polytope of Type {22,14}

Atlas Canonical Name : {22,14}*616
Also Known As : {22,14|2}. if this polytope has another name.
Group : SmallGroup(616,31)
Rank : 3
Schlafli Type : {22,14}
Number of vertices, edges, etc : 22, 154, 14
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 :
{22,14,2} of size 1232
Vertex Figure Of :
{2,22,14} of size 1232
Quotients (Maximal Quotients in Boldface) :
7-fold quotients : {22,2}*88
11-fold quotients : {2,14}*56
14-fold quotients : {11,2}*44
22-fold quotients : {2,7}*28
77-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {22,28}*1232, {44,14}*1232
3-fold covers : {22,42}*1848, {66,14}*1848
Permutation Representation (GAP) :
```s0 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)
( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)
( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)
( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)
( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)
(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)(123,132)
(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)(137,140)
(138,139)(145,154)(146,153)(147,152)(148,151)(149,150);;
s1 := (  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 68)( 13, 67)( 14, 77)
( 15, 76)( 16, 75)( 17, 74)( 18, 73)( 19, 72)( 20, 71)( 21, 70)( 22, 69)
( 23, 57)( 24, 56)( 25, 66)( 26, 65)( 27, 64)( 28, 63)( 29, 62)( 30, 61)
( 31, 60)( 32, 59)( 33, 58)( 34, 46)( 35, 45)( 36, 55)( 37, 54)( 38, 53)
( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 78, 79)( 80, 88)
( 81, 87)( 82, 86)( 83, 85)( 89,145)( 90,144)( 91,154)( 92,153)( 93,152)
( 94,151)( 95,150)( 96,149)( 97,148)( 98,147)( 99,146)(100,134)(101,133)
(102,143)(103,142)(104,141)(105,140)(106,139)(107,138)(108,137)(109,136)
(110,135)(111,123)(112,122)(113,132)(114,131)(115,130)(116,129)(117,128)
(118,127)(119,126)(120,125)(121,124);;
s2 := (  1, 89)(  2, 90)(  3, 91)(  4, 92)(  5, 93)(  6, 94)(  7, 95)(  8, 96)
(  9, 97)( 10, 98)( 11, 99)( 12, 78)( 13, 79)( 14, 80)( 15, 81)( 16, 82)
( 17, 83)( 18, 84)( 19, 85)( 20, 86)( 21, 87)( 22, 88)( 23,144)( 24,145)
( 25,146)( 26,147)( 27,148)( 28,149)( 29,150)( 30,151)( 31,152)( 32,153)
( 33,154)( 34,133)( 35,134)( 36,135)( 37,136)( 38,137)( 39,138)( 40,139)
( 41,140)( 42,141)( 43,142)( 44,143)( 45,122)( 46,123)( 47,124)( 48,125)
( 49,126)( 50,127)( 51,128)( 52,129)( 53,130)( 54,131)( 55,132)( 56,111)
( 57,112)( 58,113)( 59,114)( 60,115)( 61,116)( 62,117)( 63,118)( 64,119)
( 65,120)( 66,121)( 67,100)( 68,101)( 69,102)( 70,103)( 71,104)( 72,105)
( 73,106)( 74,107)( 75,108)( 76,109)( 77,110);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope