Polytope of Type {6,6} with group SmallGroup(600,154)

Overview

Group: SmallGroup(600,154)
Rank: 3
Schläfli Type: {6,6}
Vertices, edges, …: 50, 150, 50
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{3,6}*300

75-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*(s2*s1)^2)^2> of order 5

10 facets

10 of {6}*12

10 vertex figures

10 of {6}*12

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.