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# Polytope of Type {24,4}

Atlas Canonical Name : {24,4}*384a
if this polytope has a name.
Group : SmallGroup(384,682)
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}*192a, {12,4}*192a, {24,4}*192b
3-fold quotients : {8,4}*128a
4-fold quotients : {12,4}*96a, {24,2}*96
6-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
8-fold quotients : {12,2}*48, {6,4}*48a
12-fold quotients : {4,4}*32, {8,2}*32
16-fold quotients : {6,2}*24
24-fold quotients : {2,4}*16, {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}*768a, {24,4}*768a, {24,8}*768d, {48,4}*768a, {48,4}*768b
3-fold covers : {72,4}*1152a, {24,12}*1152a, {24,12}*1152b
5-fold covers : {120,4}*1920a, {24,20}*1920a
Permutation Representation (GAP) :
```s0 := (  1, 97)(  2, 99)(  3, 98)(  4,100)(  5,102)(  6,101)(  7,103)(  8,105)
(  9,104)( 10,106)( 11,108)( 12,107)( 13,112)( 14,114)( 15,113)( 16,109)
( 17,111)( 18,110)( 19,118)( 20,120)( 21,119)( 22,115)( 23,117)( 24,116)
( 25,127)( 26,129)( 27,128)( 28,130)( 29,132)( 30,131)( 31,121)( 32,123)
( 33,122)( 34,124)( 35,126)( 36,125)( 37,142)( 38,144)( 39,143)( 40,139)
( 41,141)( 42,140)( 43,136)( 44,138)( 45,137)( 46,133)( 47,135)( 48,134)
( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)( 56,153)
( 57,152)( 58,154)( 59,156)( 60,155)( 61,160)( 62,162)( 63,161)( 64,157)
( 65,159)( 66,158)( 67,166)( 68,168)( 69,167)( 70,163)( 71,165)( 72,164)
( 73,175)( 74,177)( 75,176)( 76,178)( 77,180)( 78,179)( 79,169)( 80,171)
( 81,170)( 82,172)( 83,174)( 84,173)( 85,190)( 86,192)( 87,191)( 88,187)
( 89,189)( 90,188)( 91,184)( 92,186)( 93,185)( 94,181)( 95,183)( 96,182);;
s1 := (  1,  2)(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 32)( 26, 31)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 37, 44)( 38, 43)
( 39, 45)( 40, 47)( 41, 46)( 42, 48)( 49, 62)( 50, 61)( 51, 63)( 52, 65)
( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)( 59, 70)( 60, 72)
( 73, 92)( 74, 91)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 86)( 80, 85)
( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 97,122)( 98,121)( 99,123)(100,125)
(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)(107,130)(108,132)
(109,134)(110,133)(111,135)(112,137)(113,136)(114,138)(115,140)(116,139)
(117,141)(118,143)(119,142)(120,144)(145,185)(146,184)(147,186)(148,182)
(149,181)(150,183)(151,191)(152,190)(153,192)(154,188)(155,187)(156,189)
(157,173)(158,172)(159,174)(160,170)(161,169)(162,171)(163,179)(164,178)
(165,180)(166,176)(167,175)(168,177);;
s2 := (  1, 49)(  2, 50)(  3, 51)(  4, 52)(  5, 53)(  6, 54)(  7, 55)(  8, 56)
(  9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 63)( 16, 64)
( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)( 24, 72)
( 25, 76)( 26, 77)( 27, 78)( 28, 73)( 29, 74)( 30, 75)( 31, 82)( 32, 83)
( 33, 84)( 34, 79)( 35, 80)( 36, 81)( 37, 88)( 38, 89)( 39, 90)( 40, 85)
( 41, 86)( 42, 87)( 43, 94)( 44, 95)( 45, 96)( 46, 91)( 47, 92)( 48, 93)
( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)
(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)(112,160)
(113,161)(114,162)(115,163)(116,164)(117,165)(118,166)(119,167)(120,168)
(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)(128,179)
(129,180)(130,175)(131,176)(132,177)(133,184)(134,185)(135,186)(136,181)
(137,182)(138,183)(139,190)(140,191)(141,192)(142,187)(143,188)(144,189);;
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*s2*s1*s2*s1*s0*s1*s0*s2*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)!(  1, 97)(  2, 99)(  3, 98)(  4,100)(  5,102)(  6,101)(  7,103)
(  8,105)(  9,104)( 10,106)( 11,108)( 12,107)( 13,112)( 14,114)( 15,113)
( 16,109)( 17,111)( 18,110)( 19,118)( 20,120)( 21,119)( 22,115)( 23,117)
( 24,116)( 25,127)( 26,129)( 27,128)( 28,130)( 29,132)( 30,131)( 31,121)
( 32,123)( 33,122)( 34,124)( 35,126)( 36,125)( 37,142)( 38,144)( 39,143)
( 40,139)( 41,141)( 42,140)( 43,136)( 44,138)( 45,137)( 46,133)( 47,135)
( 48,134)( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)
( 56,153)( 57,152)( 58,154)( 59,156)( 60,155)( 61,160)( 62,162)( 63,161)
( 64,157)( 65,159)( 66,158)( 67,166)( 68,168)( 69,167)( 70,163)( 71,165)
( 72,164)( 73,175)( 74,177)( 75,176)( 76,178)( 77,180)( 78,179)( 79,169)
( 80,171)( 81,170)( 82,172)( 83,174)( 84,173)( 85,190)( 86,192)( 87,191)
( 88,187)( 89,189)( 90,188)( 91,184)( 92,186)( 93,185)( 94,181)( 95,183)
( 96,182);
s1 := Sym(192)!(  1,  2)(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)
( 22, 23)( 25, 32)( 26, 31)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 37, 44)
( 38, 43)( 39, 45)( 40, 47)( 41, 46)( 42, 48)( 49, 62)( 50, 61)( 51, 63)
( 52, 65)( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)( 59, 70)
( 60, 72)( 73, 92)( 74, 91)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 86)
( 80, 85)( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 97,122)( 98,121)( 99,123)
(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)(107,130)
(108,132)(109,134)(110,133)(111,135)(112,137)(113,136)(114,138)(115,140)
(116,139)(117,141)(118,143)(119,142)(120,144)(145,185)(146,184)(147,186)
(148,182)(149,181)(150,183)(151,191)(152,190)(153,192)(154,188)(155,187)
(156,189)(157,173)(158,172)(159,174)(160,170)(161,169)(162,171)(163,179)
(164,178)(165,180)(166,176)(167,175)(168,177);
s2 := Sym(192)!(  1, 49)(  2, 50)(  3, 51)(  4, 52)(  5, 53)(  6, 54)(  7, 55)
(  8, 56)(  9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 63)
( 16, 64)( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)
( 24, 72)( 25, 76)( 26, 77)( 27, 78)( 28, 73)( 29, 74)( 30, 75)( 31, 82)
( 32, 83)( 33, 84)( 34, 79)( 35, 80)( 36, 81)( 37, 88)( 38, 89)( 39, 90)
( 40, 85)( 41, 86)( 42, 87)( 43, 94)( 44, 95)( 45, 96)( 46, 91)( 47, 92)
( 48, 93)( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)
(104,152)(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)
(112,160)(113,161)(114,162)(115,163)(116,164)(117,165)(118,166)(119,167)
(120,168)(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)
(128,179)(129,180)(130,175)(131,176)(132,177)(133,184)(134,185)(135,186)
(136,181)(137,182)(138,183)(139,190)(140,191)(141,192)(142,187)(143,188)
(144,189);
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*s2*s1*s2*s1*s0*s1*s0*s2*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