# Polytope of Type {4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*384c
if this polytope has a name.
Group : SmallGroup(384,18015)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 8, 96, 48
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,24,2} of size 768
Vertex Figure Of :
{2,4,24} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,24}*192c, {4,24}*192d, {4,12}*192b
4-fold quotients : {2,24}*96, {4,12}*96b, {4,12}*96c, {4,6}*96
8-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
12-fold quotients : {2,8}*32
16-fold quotients : {4,3}*24, {2,6}*24
24-fold quotients : {2,4}*16
32-fold quotients : {2,3}*12
48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,24}*768i, {8,24}*768k, {4,24}*768i, {4,48}*768c, {4,48}*768d
3-fold covers : {4,72}*1152c, {12,24}*1152o, {12,24}*1152p
5-fold covers : {20,24}*1920c, {4,120}*1920c
Permutation Representation (GAP) :
```s0 := (  1, 99)(  2,100)(  3, 97)(  4, 98)(  5,103)(  6,104)(  7,101)(  8,102)
(  9,107)( 10,108)( 11,105)( 12,106)( 13,111)( 14,112)( 15,109)( 16,110)
( 17,115)( 18,116)( 19,113)( 20,114)( 21,119)( 22,120)( 23,117)( 24,118)
( 25,123)( 26,124)( 27,121)( 28,122)( 29,127)( 30,128)( 31,125)( 32,126)
( 33,131)( 34,132)( 35,129)( 36,130)( 37,135)( 38,136)( 39,133)( 40,134)
( 41,139)( 42,140)( 43,137)( 44,138)( 45,143)( 46,144)( 47,141)( 48,142)
( 49,147)( 50,148)( 51,145)( 52,146)( 53,151)( 54,152)( 55,149)( 56,150)
( 57,155)( 58,156)( 59,153)( 60,154)( 61,159)( 62,160)( 63,157)( 64,158)
( 65,163)( 66,164)( 67,161)( 68,162)( 69,167)( 70,168)( 71,165)( 72,166)
( 73,171)( 74,172)( 75,169)( 76,170)( 77,175)( 78,176)( 79,173)( 80,174)
( 81,179)( 82,180)( 83,177)( 84,178)( 85,183)( 86,184)( 87,181)( 88,182)
( 89,187)( 90,188)( 91,185)( 92,186)( 93,191)( 94,192)( 95,189)( 96,190);;
s1 := (  2,  3)(  5,  9)(  6, 11)(  7, 10)(  8, 12)( 14, 15)( 17, 21)( 18, 23)
( 19, 22)( 20, 24)( 25, 37)( 26, 39)( 27, 38)( 28, 40)( 29, 45)( 30, 47)
( 31, 46)( 32, 48)( 33, 41)( 34, 43)( 35, 42)( 36, 44)( 49, 73)( 50, 75)
( 51, 74)( 52, 76)( 53, 81)( 54, 83)( 55, 82)( 56, 84)( 57, 77)( 58, 79)
( 59, 78)( 60, 80)( 61, 85)( 62, 87)( 63, 86)( 64, 88)( 65, 93)( 66, 95)
( 67, 94)( 68, 96)( 69, 89)( 70, 91)( 71, 90)( 72, 92)( 98, 99)(101,105)
(102,107)(103,106)(104,108)(110,111)(113,117)(114,119)(115,118)(116,120)
(121,133)(122,135)(123,134)(124,136)(125,141)(126,143)(127,142)(128,144)
(129,137)(130,139)(131,138)(132,140)(145,169)(146,171)(147,170)(148,172)
(149,177)(150,179)(151,178)(152,180)(153,173)(154,175)(155,174)(156,176)
(157,181)(158,183)(159,182)(160,184)(161,189)(162,191)(163,190)(164,192)
(165,185)(166,187)(167,186)(168,188);;
s2 := (  1, 57)(  2, 60)(  3, 59)(  4, 58)(  5, 53)(  6, 56)(  7, 55)(  8, 54)
(  9, 49)( 10, 52)( 11, 51)( 12, 50)( 13, 69)( 14, 72)( 15, 71)( 16, 70)
( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21, 61)( 22, 64)( 23, 63)( 24, 62)
( 25, 93)( 26, 96)( 27, 95)( 28, 94)( 29, 89)( 30, 92)( 31, 91)( 32, 90)
( 33, 85)( 34, 88)( 35, 87)( 36, 86)( 37, 81)( 38, 84)( 39, 83)( 40, 82)
( 41, 77)( 42, 80)( 43, 79)( 44, 78)( 45, 73)( 46, 76)( 47, 75)( 48, 74)
( 97,153)( 98,156)( 99,155)(100,154)(101,149)(102,152)(103,151)(104,150)
(105,145)(106,148)(107,147)(108,146)(109,165)(110,168)(111,167)(112,166)
(113,161)(114,164)(115,163)(116,162)(117,157)(118,160)(119,159)(120,158)
(121,189)(122,192)(123,191)(124,190)(125,185)(126,188)(127,187)(128,186)
(129,181)(130,184)(131,183)(132,182)(133,177)(134,180)(135,179)(136,178)
(137,173)(138,176)(139,175)(140,174)(141,169)(142,172)(143,171)(144,170);;
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(192)!(  1, 99)(  2,100)(  3, 97)(  4, 98)(  5,103)(  6,104)(  7,101)
(  8,102)(  9,107)( 10,108)( 11,105)( 12,106)( 13,111)( 14,112)( 15,109)
( 16,110)( 17,115)( 18,116)( 19,113)( 20,114)( 21,119)( 22,120)( 23,117)
( 24,118)( 25,123)( 26,124)( 27,121)( 28,122)( 29,127)( 30,128)( 31,125)
( 32,126)( 33,131)( 34,132)( 35,129)( 36,130)( 37,135)( 38,136)( 39,133)
( 40,134)( 41,139)( 42,140)( 43,137)( 44,138)( 45,143)( 46,144)( 47,141)
( 48,142)( 49,147)( 50,148)( 51,145)( 52,146)( 53,151)( 54,152)( 55,149)
( 56,150)( 57,155)( 58,156)( 59,153)( 60,154)( 61,159)( 62,160)( 63,157)
( 64,158)( 65,163)( 66,164)( 67,161)( 68,162)( 69,167)( 70,168)( 71,165)
( 72,166)( 73,171)( 74,172)( 75,169)( 76,170)( 77,175)( 78,176)( 79,173)
( 80,174)( 81,179)( 82,180)( 83,177)( 84,178)( 85,183)( 86,184)( 87,181)
( 88,182)( 89,187)( 90,188)( 91,185)( 92,186)( 93,191)( 94,192)( 95,189)
( 96,190);
s1 := Sym(192)!(  2,  3)(  5,  9)(  6, 11)(  7, 10)(  8, 12)( 14, 15)( 17, 21)
( 18, 23)( 19, 22)( 20, 24)( 25, 37)( 26, 39)( 27, 38)( 28, 40)( 29, 45)
( 30, 47)( 31, 46)( 32, 48)( 33, 41)( 34, 43)( 35, 42)( 36, 44)( 49, 73)
( 50, 75)( 51, 74)( 52, 76)( 53, 81)( 54, 83)( 55, 82)( 56, 84)( 57, 77)
( 58, 79)( 59, 78)( 60, 80)( 61, 85)( 62, 87)( 63, 86)( 64, 88)( 65, 93)
( 66, 95)( 67, 94)( 68, 96)( 69, 89)( 70, 91)( 71, 90)( 72, 92)( 98, 99)
(101,105)(102,107)(103,106)(104,108)(110,111)(113,117)(114,119)(115,118)
(116,120)(121,133)(122,135)(123,134)(124,136)(125,141)(126,143)(127,142)
(128,144)(129,137)(130,139)(131,138)(132,140)(145,169)(146,171)(147,170)
(148,172)(149,177)(150,179)(151,178)(152,180)(153,173)(154,175)(155,174)
(156,176)(157,181)(158,183)(159,182)(160,184)(161,189)(162,191)(163,190)
(164,192)(165,185)(166,187)(167,186)(168,188);
s2 := Sym(192)!(  1, 57)(  2, 60)(  3, 59)(  4, 58)(  5, 53)(  6, 56)(  7, 55)
(  8, 54)(  9, 49)( 10, 52)( 11, 51)( 12, 50)( 13, 69)( 14, 72)( 15, 71)
( 16, 70)( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21, 61)( 22, 64)( 23, 63)
( 24, 62)( 25, 93)( 26, 96)( 27, 95)( 28, 94)( 29, 89)( 30, 92)( 31, 91)
( 32, 90)( 33, 85)( 34, 88)( 35, 87)( 36, 86)( 37, 81)( 38, 84)( 39, 83)
( 40, 82)( 41, 77)( 42, 80)( 43, 79)( 44, 78)( 45, 73)( 46, 76)( 47, 75)
( 48, 74)( 97,153)( 98,156)( 99,155)(100,154)(101,149)(102,152)(103,151)
(104,150)(105,145)(106,148)(107,147)(108,146)(109,165)(110,168)(111,167)
(112,166)(113,161)(114,164)(115,163)(116,162)(117,157)(118,160)(119,159)
(120,158)(121,189)(122,192)(123,191)(124,190)(125,185)(126,188)(127,187)
(128,186)(129,181)(130,184)(131,183)(132,182)(133,177)(134,180)(135,179)
(136,178)(137,173)(138,176)(139,175)(140,174)(141,169)(142,172)(143,171)
(144,170);
poly := sub<Sym(192)|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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2 >;

```
References : None.
to this polytope