# Polytope of Type {8,24}

Atlas Canonical Name : {8,24}*384b
Also Known As : {8,24|2}. if this polytope has another name.
Group : SmallGroup(384,770)
Rank : 3
Schlafli Type : {8,24}
Number of vertices, edges, etc : 8, 96, 24
Order of s0s1s2 : 24
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,24,2} of size 768
Vertex Figure Of :
{2,8,24} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,24}*192a, {8,12}*192a
3-fold quotients : {8,8}*128b
4-fold quotients : {4,12}*96a, {2,24}*96, {8,6}*96
6-fold quotients : {4,8}*64a, {8,4}*64a
8-fold quotients : {2,12}*48, {4,6}*48a
12-fold quotients : {4,4}*32, {2,8}*32, {8,2}*32
16-fold quotients : {2,6}*24
24-fold quotients : {2,4}*16, {4,2}*16
32-fold quotients : {2,3}*12
48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,24}*768a, {8,48}*768d, {16,24}*768d, {8,48}*768f, {16,24}*768f
3-fold covers : {8,72}*1152c, {24,24}*1152b, {24,24}*1152h
5-fold covers : {8,120}*1920c, {40,24}*1920a
Permutation Representation (GAP) :
```s0 := (  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, 64)( 14, 65)( 15, 66)( 16, 61)
( 17, 62)( 18, 63)( 19, 70)( 20, 71)( 21, 72)( 22, 67)( 23, 68)( 24, 69)
( 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, 85)( 38, 86)( 39, 87)( 40, 88)
( 41, 89)( 42, 90)( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)( 48, 96)
( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)
(105,153)(106,154)(107,155)(108,156)(109,160)(110,161)(111,162)(112,157)
(113,158)(114,159)(115,166)(116,167)(117,168)(118,163)(119,164)(120,165)
(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)(128,179)
(129,180)(130,175)(131,176)(132,177)(133,181)(134,182)(135,183)(136,184)
(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192);;
s1 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 19, 22)
( 20, 24)( 21, 23)( 25, 31)( 26, 33)( 27, 32)( 28, 34)( 29, 36)( 30, 35)
( 37, 46)( 38, 48)( 39, 47)( 40, 43)( 41, 45)( 42, 44)( 49, 61)( 50, 63)
( 51, 62)( 52, 64)( 53, 66)( 54, 65)( 55, 67)( 56, 69)( 57, 68)( 58, 70)
( 59, 72)( 60, 71)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)( 78, 95)
( 79, 85)( 80, 87)( 81, 86)( 82, 88)( 83, 90)( 84, 89)( 97,121)( 98,123)
( 99,122)(100,124)(101,126)(102,125)(103,127)(104,129)(105,128)(106,130)
(107,132)(108,131)(109,136)(110,138)(111,137)(112,133)(113,135)(114,134)
(115,142)(116,144)(117,143)(118,139)(119,141)(120,140)(145,184)(146,186)
(147,185)(148,181)(149,183)(150,182)(151,190)(152,192)(153,191)(154,187)
(155,189)(156,188)(157,172)(158,174)(159,173)(160,169)(161,171)(162,170)
(163,178)(164,180)(165,179)(166,175)(167,177)(168,176);;
s2 := (  1,146)(  2,145)(  3,147)(  4,149)(  5,148)(  6,150)(  7,152)(  8,151)
(  9,153)( 10,155)( 11,154)( 12,156)( 13,158)( 14,157)( 15,159)( 16,161)
( 17,160)( 18,162)( 19,164)( 20,163)( 21,165)( 22,167)( 23,166)( 24,168)
( 25,179)( 26,178)( 27,180)( 28,176)( 29,175)( 30,177)( 31,173)( 32,172)
( 33,174)( 34,170)( 35,169)( 36,171)( 37,191)( 38,190)( 39,192)( 40,188)
( 41,187)( 42,189)( 43,185)( 44,184)( 45,186)( 46,182)( 47,181)( 48,183)
( 49, 98)( 50, 97)( 51, 99)( 52,101)( 53,100)( 54,102)( 55,104)( 56,103)
( 57,105)( 58,107)( 59,106)( 60,108)( 61,110)( 62,109)( 63,111)( 64,113)
( 65,112)( 66,114)( 67,116)( 68,115)( 69,117)( 70,119)( 71,118)( 72,120)
( 73,131)( 74,130)( 75,132)( 76,128)( 77,127)( 78,129)( 79,125)( 80,124)
( 81,126)( 82,122)( 83,121)( 84,123)( 85,143)( 86,142)( 87,144)( 88,140)
( 89,139)( 90,141)( 91,137)( 92,136)( 93,138)( 94,134)( 95,133)( 96,135);;
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*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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, 49)(  2, 50)(  3, 51)(  4, 52)(  5, 53)(  6, 54)(  7, 55)
(  8, 56)(  9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 64)( 14, 65)( 15, 66)
( 16, 61)( 17, 62)( 18, 63)( 19, 70)( 20, 71)( 21, 72)( 22, 67)( 23, 68)
( 24, 69)( 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, 85)( 38, 86)( 39, 87)
( 40, 88)( 41, 89)( 42, 90)( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)
( 48, 96)( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)
(104,152)(105,153)(106,154)(107,155)(108,156)(109,160)(110,161)(111,162)
(112,157)(113,158)(114,159)(115,166)(116,167)(117,168)(118,163)(119,164)
(120,165)(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)
(128,179)(129,180)(130,175)(131,176)(132,177)(133,181)(134,182)(135,183)
(136,184)(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)
(144,192);
s1 := Sym(192)!(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 19, 22)( 20, 24)( 21, 23)( 25, 31)( 26, 33)( 27, 32)( 28, 34)( 29, 36)
( 30, 35)( 37, 46)( 38, 48)( 39, 47)( 40, 43)( 41, 45)( 42, 44)( 49, 61)
( 50, 63)( 51, 62)( 52, 64)( 53, 66)( 54, 65)( 55, 67)( 56, 69)( 57, 68)
( 58, 70)( 59, 72)( 60, 71)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)
( 78, 95)( 79, 85)( 80, 87)( 81, 86)( 82, 88)( 83, 90)( 84, 89)( 97,121)
( 98,123)( 99,122)(100,124)(101,126)(102,125)(103,127)(104,129)(105,128)
(106,130)(107,132)(108,131)(109,136)(110,138)(111,137)(112,133)(113,135)
(114,134)(115,142)(116,144)(117,143)(118,139)(119,141)(120,140)(145,184)
(146,186)(147,185)(148,181)(149,183)(150,182)(151,190)(152,192)(153,191)
(154,187)(155,189)(156,188)(157,172)(158,174)(159,173)(160,169)(161,171)
(162,170)(163,178)(164,180)(165,179)(166,175)(167,177)(168,176);
s2 := Sym(192)!(  1,146)(  2,145)(  3,147)(  4,149)(  5,148)(  6,150)(  7,152)
(  8,151)(  9,153)( 10,155)( 11,154)( 12,156)( 13,158)( 14,157)( 15,159)
( 16,161)( 17,160)( 18,162)( 19,164)( 20,163)( 21,165)( 22,167)( 23,166)
( 24,168)( 25,179)( 26,178)( 27,180)( 28,176)( 29,175)( 30,177)( 31,173)
( 32,172)( 33,174)( 34,170)( 35,169)( 36,171)( 37,191)( 38,190)( 39,192)
( 40,188)( 41,187)( 42,189)( 43,185)( 44,184)( 45,186)( 46,182)( 47,181)
( 48,183)( 49, 98)( 50, 97)( 51, 99)( 52,101)( 53,100)( 54,102)( 55,104)
( 56,103)( 57,105)( 58,107)( 59,106)( 60,108)( 61,110)( 62,109)( 63,111)
( 64,113)( 65,112)( 66,114)( 67,116)( 68,115)( 69,117)( 70,119)( 71,118)
( 72,120)( 73,131)( 74,130)( 75,132)( 76,128)( 77,127)( 78,129)( 79,125)
( 80,124)( 81,126)( 82,122)( 83,121)( 84,123)( 85,143)( 86,142)( 87,144)
( 88,140)( 89,139)( 90,141)( 91,137)( 92,136)( 93,138)( 94,134)( 95,133)
( 96,135);
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*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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