# Polytope of Type {24,4}

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