Polytope of Type {10,20} with group SmallGroup(1280,1116454)

Overview

Group: SmallGroup(1280,1116454)
Rank: 3
Schläfli Type: {10,20}
Vertices, edges, …: 32, 320, 64
Order of s₀s₁s₂: 4
Order of s₀s₁s₂s₁: 20
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

{5,5}*160

160-fold

{2,2}*8

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=<s1*s0*(s2*s1)^2*s0*s1*s0*(s2*s1)^2*s2> of order 2

32 facets

32 of {10}*20

16 vertex figures

16 of {20}*40

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

32 facets

32 of {10}*20

16 vertex figures

16 of {20}*40

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.