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# Polytope of Type {24,8}

Atlas Canonical Name : {24,8}*384d
if this polytope has a name.
Group : SmallGroup(384,966)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 24, 96, 8
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{24,8,2} of size 768
Vertex Figure Of :
{2,24,8} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {24,4}*192b, {12,8}*192a
3-fold quotients : {8,8}*128a
4-fold quotients : {12,4}*96a, {6,8}*96
6-fold quotients : {4,8}*64a, {8,4}*64b
8-fold quotients : {12,2}*48, {6,4}*48a
12-fold quotients : {4,4}*32, {2,8}*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, {48,8}*768a, {48,8}*768b, {24,16}*768c, {24,16}*768e
3-fold covers : {72,8}*1152a, {24,24}*1152d, {24,24}*1152i
5-fold covers : {120,8}*1920a, {24,40}*1920c
Permutation Representation (GAP) :
```s0 := (  1, 49)(  2, 51)(  3, 50)(  4, 52)(  5, 54)(  6, 53)(  7, 55)(  8, 57)
(  9, 56)( 10, 58)( 11, 60)( 12, 59)( 13, 64)( 14, 66)( 15, 65)( 16, 61)
( 17, 63)( 18, 62)( 19, 70)( 20, 72)( 21, 71)( 22, 67)( 23, 69)( 24, 68)
( 25, 76)( 26, 78)( 27, 77)( 28, 73)( 29, 75)( 30, 74)( 31, 82)( 32, 84)
( 33, 83)( 34, 79)( 35, 81)( 36, 80)( 37, 85)( 38, 87)( 39, 86)( 40, 88)
( 41, 90)( 42, 89)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 96)( 48, 95)
( 97,145)( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,151)(104,153)
(105,152)(106,154)(107,156)(108,155)(109,160)(110,162)(111,161)(112,157)
(113,159)(114,158)(115,166)(116,168)(117,167)(118,163)(119,165)(120,164)
(121,172)(122,174)(123,173)(124,169)(125,171)(126,170)(127,178)(128,180)
(129,179)(130,175)(131,177)(132,176)(133,181)(134,183)(135,182)(136,184)
(137,186)(138,185)(139,187)(140,189)(141,188)(142,190)(143,192)(144,191);;
s1 := (  1,  2)(  4,  5)(  7,  8)( 10, 11)( 13, 17)( 14, 16)( 15, 18)( 19, 23)
( 20, 22)( 21, 24)( 25, 32)( 26, 31)( 27, 33)( 28, 35)( 29, 34)( 30, 36)
( 37, 47)( 38, 46)( 39, 48)( 40, 44)( 41, 43)( 42, 45)( 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)(109,137)(110,136)(111,138)(112,134)(113,133)(114,135)
(115,143)(116,142)(117,144)(118,140)(119,139)(120,141)(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, 97)(  2, 98)(  3, 99)(  4,100)(  5,101)(  6,102)(  7,103)(  8,104)
(  9,105)( 10,106)( 11,107)( 12,108)( 13,112)( 14,113)( 15,114)( 16,109)
( 17,110)( 18,111)( 19,118)( 20,119)( 21,120)( 22,115)( 23,116)( 24,117)
( 25,127)( 26,128)( 27,129)( 28,130)( 29,131)( 30,132)( 31,121)( 32,122)
( 33,123)( 34,124)( 35,125)( 36,126)( 37,142)( 38,143)( 39,144)( 40,139)
( 41,140)( 42,141)( 43,136)( 44,137)( 45,138)( 46,133)( 47,134)( 48,135)
( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)
( 57,153)( 58,154)( 59,155)( 60,156)( 61,160)( 62,161)( 63,162)( 64,157)
( 65,158)( 66,159)( 67,166)( 68,167)( 69,168)( 70,163)( 71,164)( 72,165)
( 73,175)( 74,176)( 75,177)( 76,178)( 77,179)( 78,180)( 79,169)( 80,170)
( 81,171)( 82,172)( 83,173)( 84,174)( 85,190)( 86,191)( 87,192)( 88,187)
( 89,188)( 90,189)( 91,184)( 92,185)( 93,186)( 94,181)( 95,182)( 96,183);;
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*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;

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

```
References : None.
to this polytope