# Polytope of Type {24,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,10}*480
Also Known As : {24,10|2}. if this polytope has another name.
Group : SmallGroup(480,324)
Rank : 3
Schlafli Type : {24,10}
Number of vertices, edges, etc : 24, 120, 10
Order of s0s1s2 : 120
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{24,10,2} of size 960
{24,10,4} of size 1920
Vertex Figure Of :
{2,24,10} of size 960
{4,24,10} of size 1920
{4,24,10} of size 1920
{4,24,10} of size 1920
{4,24,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,10}*240
3-fold quotients : {8,10}*160
4-fold quotients : {6,10}*120
5-fold quotients : {24,2}*96
6-fold quotients : {4,10}*80
10-fold quotients : {12,2}*48
12-fold quotients : {2,10}*40
15-fold quotients : {8,2}*32
20-fold quotients : {6,2}*24
24-fold quotients : {2,5}*20
30-fold quotients : {4,2}*16
40-fold quotients : {3,2}*12
60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {48,10}*960, {24,20}*960a
3-fold covers : {72,10}*1440, {24,30}*1440a, {24,30}*1440b
4-fold covers : {24,20}*1920a, {24,40}*1920a, {24,40}*1920b, {48,20}*1920a, {48,20}*1920b, {96,10}*1920, {24,20}*1920c
Permutation Representation (GAP) :
```s0 := (  6, 11)(  7, 12)(  8, 13)(  9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)
( 24, 29)( 25, 30)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 56)
( 37, 57)( 38, 58)( 39, 59)( 40, 60)( 41, 51)( 42, 52)( 43, 53)( 44, 54)
( 45, 55)( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66,101)( 67,102)
( 68,103)( 69,104)( 70,105)( 71, 96)( 72, 97)( 73, 98)( 74, 99)( 75,100)
( 76,106)( 77,107)( 78,108)( 79,109)( 80,110)( 81,116)( 82,117)( 83,118)
( 84,119)( 85,120)( 86,111)( 87,112)( 88,113)( 89,114)( 90,115);;
s1 := (  1, 66)(  2, 70)(  3, 69)(  4, 68)(  5, 67)(  6, 61)(  7, 65)(  8, 64)
(  9, 63)( 10, 62)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 81)
( 17, 85)( 18, 84)( 19, 83)( 20, 82)( 21, 76)( 22, 80)( 23, 79)( 24, 78)
( 25, 77)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31,111)( 32,115)
( 33,114)( 34,113)( 35,112)( 36,106)( 37,110)( 38,109)( 39,108)( 40,107)
( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46, 96)( 47,100)( 48, 99)
( 49, 98)( 50, 97)( 51, 91)( 52, 95)( 53, 94)( 54, 93)( 55, 92)( 56,101)
( 57,105)( 58,104)( 59,103)( 60,102);;
s2 := (  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)
( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)
( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)
( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)( 78, 80)
( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)
(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)(118,120);;
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,
s1*s2*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope