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# Polytope of Type {32,6}

Atlas Canonical Name : {32,6}*384
Also Known As : {32,6|2}. if this polytope has another name.
Group : SmallGroup(384,1951)
Rank : 3
Schlafli Type : {32,6}
Number of vertices, edges, etc : 32, 96, 6
Order of s0s1s2 : 96
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{32,6,2} of size 768
{32,6,3} of size 1152
Vertex Figure Of :
{2,32,6} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {16,6}*192
3-fold quotients : {32,2}*128
4-fold quotients : {8,6}*96
6-fold quotients : {16,2}*64
8-fold quotients : {4,6}*48a
12-fold quotients : {8,2}*32
16-fold quotients : {2,6}*24
24-fold quotients : {4,2}*16
32-fold quotients : {2,3}*12
48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {32,12}*768a, {64,6}*768
3-fold covers : {32,18}*1152, {96,6}*1152a, {96,6}*1152c
5-fold covers : {32,30}*1920, {160,6}*1920
Permutation Representation (GAP) :
```s0 := (  7, 10)(  8, 11)(  9, 12)( 13, 19)( 14, 20)( 15, 21)( 16, 22)( 17, 23)
( 18, 24)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 46)
( 32, 47)( 33, 48)( 34, 43)( 35, 44)( 36, 45)( 55, 58)( 56, 59)( 57, 60)
( 61, 67)( 62, 68)( 63, 69)( 64, 70)( 65, 71)( 66, 72)( 73, 85)( 74, 86)
( 75, 87)( 76, 88)( 77, 89)( 78, 90)( 79, 94)( 80, 95)( 81, 96)( 82, 91)
( 83, 92)( 84, 93)( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)
(103,130)(104,131)(105,132)(106,127)(107,128)(108,129)(109,139)(110,140)
(111,141)(112,142)(113,143)(114,144)(115,133)(116,134)(117,135)(118,136)
(119,137)(120,138)(145,169)(146,170)(147,171)(148,172)(149,173)(150,174)
(151,178)(152,179)(153,180)(154,175)(155,176)(156,177)(157,187)(158,188)
(159,189)(160,190)(161,191)(162,192)(163,181)(164,182)(165,183)(166,184)
(167,185)(168,186);;
s1 := (  1,145)(  2,147)(  3,146)(  4,148)(  5,150)(  6,149)(  7,154)(  8,156)
(  9,155)( 10,151)( 11,153)( 12,152)( 13,163)( 14,165)( 15,164)( 16,166)
( 17,168)( 18,167)( 19,157)( 20,159)( 21,158)( 22,160)( 23,162)( 24,161)
( 25,181)( 26,183)( 27,182)( 28,184)( 29,186)( 30,185)( 31,190)( 32,192)
( 33,191)( 34,187)( 35,189)( 36,188)( 37,169)( 38,171)( 39,170)( 40,172)
( 41,174)( 42,173)( 43,178)( 44,180)( 45,179)( 46,175)( 47,177)( 48,176)
( 49, 97)( 50, 99)( 51, 98)( 52,100)( 53,102)( 54,101)( 55,106)( 56,108)
( 57,107)( 58,103)( 59,105)( 60,104)( 61,115)( 62,117)( 63,116)( 64,118)
( 65,120)( 66,119)( 67,109)( 68,111)( 69,110)( 70,112)( 71,114)( 72,113)
( 73,133)( 74,135)( 75,134)( 76,136)( 77,138)( 78,137)( 79,142)( 80,144)
( 81,143)( 82,139)( 83,141)( 84,140)( 85,121)( 86,123)( 87,122)( 88,124)
( 89,126)( 90,125)( 91,130)( 92,132)( 93,131)( 94,127)( 95,129)( 96,128);;
s2 := (  1, 50)(  2, 49)(  3, 51)(  4, 53)(  5, 52)(  6, 54)(  7, 56)(  8, 55)
(  9, 57)( 10, 59)( 11, 58)( 12, 60)( 13, 62)( 14, 61)( 15, 63)( 16, 65)
( 17, 64)( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 71)( 23, 70)( 24, 72)
( 25, 74)( 26, 73)( 27, 75)( 28, 77)( 29, 76)( 30, 78)( 31, 80)( 32, 79)
( 33, 81)( 34, 83)( 35, 82)( 36, 84)( 37, 86)( 38, 85)( 39, 87)( 40, 89)
( 41, 88)( 42, 90)( 43, 92)( 44, 91)( 45, 93)( 46, 95)( 47, 94)( 48, 96)
( 97,146)( 98,145)( 99,147)(100,149)(101,148)(102,150)(103,152)(104,151)
(105,153)(106,155)(107,154)(108,156)(109,158)(110,157)(111,159)(112,161)
(113,160)(114,162)(115,164)(116,163)(117,165)(118,167)(119,166)(120,168)
(121,170)(122,169)(123,171)(124,173)(125,172)(126,174)(127,176)(128,175)
(129,177)(130,179)(131,178)(132,180)(133,182)(134,181)(135,183)(136,185)
(137,184)(138,186)(139,188)(140,187)(141,189)(142,191)(143,190)(144,192);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope