Polytope of Type {20,6} with group SmallGroup(1200,985)

Overview

Group: SmallGroup(1200,985)
Rank: 3
Schläfli Type: {20,6}
Vertices, edges, …: 100, 300, 30
Order of s₀s₁s₂: 3
Order of s₀s₁s₂s₁: 20
Also known as: {20,6}₃. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

4-fold

{10,6}*300

25-fold

{4,6}*48b

50-fold

{4,3}*24

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^10> of order 2

20 facets

10 of {10}*20
10 of {20}*40

50 vertex figures

50 of {6}*12

P/N, where N=<(s0*s1)^2*s2*(s1*s0)^3*s1*s2*s1*s0*s1> of order 5

6 facets

6 of {20}*40

20 vertex figures

20 of {6}*12

P/N, where N=<(s0*s1)^4> of order 5

14 facets

10 of {4}*8
4 of {20}*40

20 vertex figures

20 of {6}*12

Representations

Permutation Representation (GAP)

s0 := (  1, 51)(  2, 55)(  3, 54)(  4, 53)(  5, 52)(  6, 71)(  7, 75)(  8, 74)(  9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)( 16, 61)( 17, 65)( 18, 64)( 19, 63)( 20, 62)( 21, 56)( 22, 60)( 23, 59)( 24, 58)( 25, 57)( 26, 76)( 27, 80)( 28, 79)( 29, 78)( 30, 77)( 31, 96)( 32,100)( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)( 40, 92)( 41, 86)( 42, 90)( 43, 89)( 44, 88)( 45, 87)( 46, 81)( 47, 85)( 48, 84)( 49, 83)( 50, 82);;
s1 := (  1,  2)(  3,  5)(  6,  8)(  9, 10)( 11, 14)( 12, 13)( 16, 20)( 17, 19)( 22, 25)( 23, 24)( 26, 27)( 28, 30)( 31, 33)( 34, 35)( 36, 39)( 37, 38)( 41, 45)( 42, 44)( 47, 50)( 48, 49)( 51, 77)( 52, 76)( 53, 80)( 54, 79)( 55, 78)( 56, 83)( 57, 82)( 58, 81)( 59, 85)( 60, 84)( 61, 89)( 62, 88)( 63, 87)( 64, 86)( 65, 90)( 66, 95)( 67, 94)( 68, 93)( 69, 92)( 70, 91)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97);;
s2 := (  2, 25)(  3, 19)(  4, 13)(  5,  7)(  8, 24)(  9, 18)( 10, 12)( 14, 23)( 15, 17)( 20, 22)( 26, 76)( 27,100)( 28, 94)( 29, 88)( 30, 82)( 31, 81)( 32, 80)( 33, 99)( 34, 93)( 35, 87)( 36, 86)( 37, 85)( 38, 79)( 39, 98)( 40, 92)( 41, 91)( 42, 90)( 43, 84)( 44, 78)( 45, 97)( 46, 96)( 47, 95)( 48, 89)( 49, 83)( 50, 77)( 52, 75)( 53, 69)( 54, 63)( 55, 57)( 58, 74)( 59, 68)( 60, 62)( 64, 73)( 65, 67)( 70, 72);;
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*s0*s1*s2*s0*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 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(100)!(  1, 51)(  2, 55)(  3, 54)(  4, 53)(  5, 52)(  6, 71)(  7, 75)(  8, 74)(  9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)( 16, 61)( 17, 65)( 18, 64)( 19, 63)( 20, 62)( 21, 56)( 22, 60)( 23, 59)( 24, 58)( 25, 57)( 26, 76)( 27, 80)( 28, 79)( 29, 78)( 30, 77)( 31, 96)( 32,100)( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)( 40, 92)( 41, 86)( 42, 90)( 43, 89)( 44, 88)( 45, 87)( 46, 81)( 47, 85)( 48, 84)( 49, 83)( 50, 82);
s1 := Sym(100)!(  1,  2)(  3,  5)(  6,  8)(  9, 10)( 11, 14)( 12, 13)( 16, 20)( 17, 19)( 22, 25)( 23, 24)( 26, 27)( 28, 30)( 31, 33)( 34, 35)( 36, 39)( 37, 38)( 41, 45)( 42, 44)( 47, 50)( 48, 49)( 51, 77)( 52, 76)( 53, 80)( 54, 79)( 55, 78)( 56, 83)( 57, 82)( 58, 81)( 59, 85)( 60, 84)( 61, 89)( 62, 88)( 63, 87)( 64, 86)( 65, 90)( 66, 95)( 67, 94)( 68, 93)( 69, 92)( 70, 91)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97);
s2 := Sym(100)!(  2, 25)(  3, 19)(  4, 13)(  5,  7)(  8, 24)(  9, 18)( 10, 12)( 14, 23)( 15, 17)( 20, 22)( 26, 76)( 27,100)( 28, 94)( 29, 88)( 30, 82)( 31, 81)( 32, 80)( 33, 99)( 34, 93)( 35, 87)( 36, 86)( 37, 85)( 38, 79)( 39, 98)( 40, 92)( 41, 91)( 42, 90)( 43, 84)( 44, 78)( 45, 97)( 46, 96)( 47, 95)( 48, 89)( 49, 83)( 50, 77)( 52, 75)( 53, 69)( 54, 63)( 55, 57)( 58, 74)( 59, 68)( 60, 62)( 64, 73)( 65, 67)( 70, 72);
poly := sub<Sym(100)|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*s0*s1*s2*s0*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 >;

References

None.

to this polytope.