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# Polytope of Type {2,8,24}

Atlas Canonical Name : {2,8,24}*768d
if this polytope has a name.
Group : SmallGroup(768,150684)
Rank : 4
Schlafli Type : {2,8,24}
Number of vertices, edges, etc : 2, 8, 96, 24
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,24}*384b, {2,8,12}*384b
3-fold quotients : {2,8,8}*256d
4-fold quotients : {2,4,12}*192a
6-fold quotients : {2,4,8}*128b, {2,8,4}*128b
8-fold quotients : {2,2,12}*96, {2,4,6}*96a
12-fold quotients : {2,4,4}*64
16-fold quotients : {2,2,6}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*32
32-fold quotients : {2,2,3}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (  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, 72)( 16, 73)( 17, 74)( 18, 69)
( 19, 70)( 20, 71)( 21, 66)( 22, 67)( 23, 68)( 24, 63)( 25, 64)( 26, 65)
( 27, 78)( 28, 79)( 29, 80)( 30, 75)( 31, 76)( 32, 77)( 33, 84)( 34, 85)
( 35, 86)( 36, 81)( 37, 82)( 38, 83)( 39, 93)( 40, 94)( 41, 95)( 42, 96)
( 43, 97)( 44, 98)( 45, 87)( 46, 88)( 47, 89)( 48, 90)( 49, 91)( 50, 92)
( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)
(107,155)(108,156)(109,157)(110,158)(111,168)(112,169)(113,170)(114,165)
(115,166)(116,167)(117,162)(118,163)(119,164)(120,159)(121,160)(122,161)
(123,174)(124,175)(125,176)(126,171)(127,172)(128,173)(129,180)(130,181)
(131,182)(132,177)(133,178)(134,179)(135,189)(136,190)(137,191)(138,192)
(139,193)(140,194)(141,183)(142,184)(143,185)(144,186)(145,187)(146,188);;
s2 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 15, 24)( 16, 26)( 17, 25)( 18, 21)
( 19, 23)( 20, 22)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 31, 38)( 32, 37)
( 39, 42)( 40, 44)( 41, 43)( 45, 48)( 46, 50)( 47, 49)( 51, 63)( 52, 65)
( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)( 59, 70)( 60, 72)
( 61, 74)( 62, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)
( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 85, 92)( 86, 91)( 99,123)(100,125)
(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)(107,130)(108,132)
(109,134)(110,133)(111,144)(112,146)(113,145)(114,141)(115,143)(116,142)
(117,138)(118,140)(119,139)(120,135)(121,137)(122,136)(147,186)(148,188)
(149,187)(150,183)(151,185)(152,184)(153,192)(154,194)(155,193)(156,189)
(157,191)(158,190)(159,174)(160,176)(161,175)(162,171)(163,173)(164,172)
(165,180)(166,182)(167,181)(168,177)(169,179)(170,178);;
s3 := (  3,100)(  4, 99)(  5,101)(  6,103)(  7,102)(  8,104)(  9,106)( 10,105)
( 11,107)( 12,109)( 13,108)( 14,110)( 15,115)( 16,114)( 17,116)( 18,112)
( 19,111)( 20,113)( 21,121)( 22,120)( 23,122)( 24,118)( 25,117)( 26,119)
( 27,130)( 28,129)( 29,131)( 30,133)( 31,132)( 32,134)( 33,124)( 34,123)
( 35,125)( 36,127)( 37,126)( 38,128)( 39,145)( 40,144)( 41,146)( 42,142)
( 43,141)( 44,143)( 45,139)( 46,138)( 47,140)( 48,136)( 49,135)( 50,137)
( 51,148)( 52,147)( 53,149)( 54,151)( 55,150)( 56,152)( 57,154)( 58,153)
( 59,155)( 60,157)( 61,156)( 62,158)( 63,163)( 64,162)( 65,164)( 66,160)
( 67,159)( 68,161)( 69,169)( 70,168)( 71,170)( 72,166)( 73,165)( 74,167)
( 75,178)( 76,177)( 77,179)( 78,181)( 79,180)( 80,182)( 81,172)( 82,171)
( 83,173)( 84,175)( 85,174)( 86,176)( 87,193)( 88,192)( 89,194)( 90,190)
( 91,189)( 92,191)( 93,187)( 94,186)( 95,188)( 96,184)( 97,183)( 98,185);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s2*s1*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(194)!(1,2);
s1 := Sym(194)!(  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, 72)( 16, 73)( 17, 74)
( 18, 69)( 19, 70)( 20, 71)( 21, 66)( 22, 67)( 23, 68)( 24, 63)( 25, 64)
( 26, 65)( 27, 78)( 28, 79)( 29, 80)( 30, 75)( 31, 76)( 32, 77)( 33, 84)
( 34, 85)( 35, 86)( 36, 81)( 37, 82)( 38, 83)( 39, 93)( 40, 94)( 41, 95)
( 42, 96)( 43, 97)( 44, 98)( 45, 87)( 46, 88)( 47, 89)( 48, 90)( 49, 91)
( 50, 92)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)
(106,154)(107,155)(108,156)(109,157)(110,158)(111,168)(112,169)(113,170)
(114,165)(115,166)(116,167)(117,162)(118,163)(119,164)(120,159)(121,160)
(122,161)(123,174)(124,175)(125,176)(126,171)(127,172)(128,173)(129,180)
(130,181)(131,182)(132,177)(133,178)(134,179)(135,189)(136,190)(137,191)
(138,192)(139,193)(140,194)(141,183)(142,184)(143,185)(144,186)(145,187)
(146,188);
s2 := Sym(194)!(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 15, 24)( 16, 26)( 17, 25)
( 18, 21)( 19, 23)( 20, 22)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 31, 38)
( 32, 37)( 39, 42)( 40, 44)( 41, 43)( 45, 48)( 46, 50)( 47, 49)( 51, 63)
( 52, 65)( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)( 59, 70)
( 60, 72)( 61, 74)( 62, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)
( 80, 97)( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 85, 92)( 86, 91)( 99,123)
(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)(107,130)
(108,132)(109,134)(110,133)(111,144)(112,146)(113,145)(114,141)(115,143)
(116,142)(117,138)(118,140)(119,139)(120,135)(121,137)(122,136)(147,186)
(148,188)(149,187)(150,183)(151,185)(152,184)(153,192)(154,194)(155,193)
(156,189)(157,191)(158,190)(159,174)(160,176)(161,175)(162,171)(163,173)
(164,172)(165,180)(166,182)(167,181)(168,177)(169,179)(170,178);
s3 := Sym(194)!(  3,100)(  4, 99)(  5,101)(  6,103)(  7,102)(  8,104)(  9,106)
( 10,105)( 11,107)( 12,109)( 13,108)( 14,110)( 15,115)( 16,114)( 17,116)
( 18,112)( 19,111)( 20,113)( 21,121)( 22,120)( 23,122)( 24,118)( 25,117)
( 26,119)( 27,130)( 28,129)( 29,131)( 30,133)( 31,132)( 32,134)( 33,124)
( 34,123)( 35,125)( 36,127)( 37,126)( 38,128)( 39,145)( 40,144)( 41,146)
( 42,142)( 43,141)( 44,143)( 45,139)( 46,138)( 47,140)( 48,136)( 49,135)
( 50,137)( 51,148)( 52,147)( 53,149)( 54,151)( 55,150)( 56,152)( 57,154)
( 58,153)( 59,155)( 60,157)( 61,156)( 62,158)( 63,163)( 64,162)( 65,164)
( 66,160)( 67,159)( 68,161)( 69,169)( 70,168)( 71,170)( 72,166)( 73,165)
( 74,167)( 75,178)( 76,177)( 77,179)( 78,181)( 79,180)( 80,182)( 81,172)
( 82,171)( 83,173)( 84,175)( 85,174)( 86,176)( 87,193)( 88,192)( 89,194)
( 90,190)( 91,189)( 92,191)( 93,187)( 94,186)( 95,188)( 96,184)( 97,183)
( 98,185);
poly := sub<Sym(194)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s2*s1*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3 >;

```

to this polytope