Polytope of Type {10,20} with group SmallGroup(400,170)

Overview

Group: SmallGroup(400,170)
Rank: 3
Schläfli Type: {10,20}
Vertices, edges, …: 10, 100, 20
Order of s₀s₁s₂: 20
Order of s₀s₁s₂s₁: 2
Also known as: {10,20|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{10,10}*200a

5-fold

10-fold

20-fold

25-fold

{2,4}*16

50-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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