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# Polytope of Type {30,10}

Atlas Canonical Name : {30,10}*600b
Also Known As : {30,10|2}. if this polytope has another name.
Group : SmallGroup(600,195)
Rank : 3
Schlafli Type : {30,10}
Number of vertices, edges, etc : 30, 150, 10
Order of s0s1s2 : 30
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{30,10,2} of size 1200
Vertex Figure Of :
{2,30,10} of size 1200
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {10,10}*200a
5-fold quotients : {6,10}*120, {30,2}*120
10-fold quotients : {15,2}*60
15-fold quotients : {2,10}*40, {10,2}*40
25-fold quotients : {6,2}*24
30-fold quotients : {2,5}*20, {5,2}*20
50-fold quotients : {3,2}*12
75-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {30,20}*1200b, {60,10}*1200b
3-fold covers : {90,10}*1800b, {30,30}*1800a, {30,30}*1800g
Permutation Representation (GAP) :
```s0 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 26, 51)( 27, 55)( 28, 54)( 29, 53)( 30, 52)( 31, 56)
( 32, 60)( 33, 59)( 34, 58)( 35, 57)( 36, 61)( 37, 65)( 38, 64)( 39, 63)
( 40, 62)( 41, 66)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 71)( 47, 75)
( 48, 74)( 49, 73)( 50, 72)( 77, 80)( 78, 79)( 82, 85)( 83, 84)( 87, 90)
( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)(101,126)(102,130)(103,129)
(104,128)(105,127)(106,131)(107,135)(108,134)(109,133)(110,132)(111,136)
(112,140)(113,139)(114,138)(115,137)(116,141)(117,145)(118,144)(119,143)
(120,142)(121,146)(122,150)(123,149)(124,148)(125,147);;
s1 := (  1, 27)(  2, 26)(  3, 30)(  4, 29)(  5, 28)(  6, 47)(  7, 46)(  8, 50)
(  9, 49)( 10, 48)( 11, 42)( 12, 41)( 13, 45)( 14, 44)( 15, 43)( 16, 37)
( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)( 24, 34)
( 25, 33)( 51, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)
( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76,102)( 77,101)( 78,105)
( 79,104)( 80,103)( 81,122)( 82,121)( 83,125)( 84,124)( 85,123)( 86,117)
( 87,116)( 88,120)( 89,119)( 90,118)( 91,112)( 92,111)( 93,115)( 94,114)
( 95,113)( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(126,127)(128,130)
(131,147)(132,146)(133,150)(134,149)(135,148)(136,142)(137,141)(138,145)
(139,144)(140,143);;
s2 := (  1, 81)(  2, 82)(  3, 83)(  4, 84)(  5, 85)(  6, 76)(  7, 77)(  8, 78)
(  9, 79)( 10, 80)( 11, 96)( 12, 97)( 13, 98)( 14, 99)( 15,100)( 16, 91)
( 17, 92)( 18, 93)( 19, 94)( 20, 95)( 21, 86)( 22, 87)( 23, 88)( 24, 89)
( 25, 90)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,101)( 32,102)
( 33,103)( 34,104)( 35,105)( 36,121)( 37,122)( 38,123)( 39,124)( 40,125)
( 41,116)( 42,117)( 43,118)( 44,119)( 45,120)( 46,111)( 47,112)( 48,113)
( 49,114)( 50,115)( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)( 56,126)
( 57,127)( 58,128)( 59,129)( 60,130)( 61,146)( 62,147)( 63,148)( 64,149)
( 65,150)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,136)( 72,137)
( 73,138)( 74,139)( 75,140);;
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*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,
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope