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

Overview

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

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

4-fold

{6,10}*300

25-fold

{6,4}*48b

50-fold

{3,4}*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)^2*(s2*s1)^8*s0*s1*s2> of order 2

50 facets

50 of {6}*12

20 vertex figures

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

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

20 facets

20 of {6}*12

6 vertex figures

6 of {20}*40

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

20 facets

20 of {6}*12

14 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.