Questions?
See the FAQ
or other info.

Polytope of Type {16,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,12}*384a
Also Known As : {16,12|2}. if this polytope has another name.
Group : SmallGroup(384,1767)
Rank : 3
Schlafli Type : {16,12}
Number of vertices, edges, etc : 16, 96, 12
Order of s0s1s2 : 48
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{16,12,2} of size 768
Vertex Figure Of :
{2,16,12} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,12}*192a, {16,6}*192
3-fold quotients : {16,4}*128a
4-fold quotients : {4,12}*96a, {8,6}*96
6-fold quotients : {8,4}*64a, {16,2}*64
8-fold quotients : {2,12}*48, {4,6}*48a
12-fold quotients : {4,4}*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 : {16,12}*768a, {16,24}*768c, {16,24}*768d, {32,12}*768a, {32,12}*768b
3-fold covers : {16,36}*1152a, {48,12}*1152b, {48,12}*1152c
5-fold covers : {16,60}*1920a, {80,12}*1920a
Permutation Representation (GAP) :
```s0 := (  1, 97)(  2, 98)(  3, 99)(  4,100)(  5,101)(  6,102)(  7,106)(  8,107)
(  9,108)( 10,103)( 11,104)( 12,105)( 13,109)( 14,110)( 15,111)( 16,112)
( 17,113)( 18,114)( 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)( 37,139)( 38,140)( 39,141)( 40,142)
( 41,143)( 42,144)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)
( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,154)( 56,155)
( 57,156)( 58,151)( 59,152)( 60,153)( 61,157)( 62,158)( 63,159)( 64,160)
( 65,161)( 66,162)( 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)( 85,187)( 86,188)( 87,189)( 88,190)
( 89,191)( 90,192)( 91,181)( 92,182)( 93,183)( 94,184)( 95,185)( 96,186);;
s1 := (  2,  3)(  5,  6)(  7, 10)(  8, 12)(  9, 11)( 14, 15)( 17, 18)( 19, 22)
( 20, 24)( 21, 23)( 25, 31)( 26, 33)( 27, 32)( 28, 34)( 29, 36)( 30, 35)
( 37, 43)( 38, 45)( 39, 44)( 40, 46)( 41, 48)( 42, 47)( 49, 61)( 50, 63)
( 51, 62)( 52, 64)( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)( 58, 67)
( 59, 69)( 60, 68)( 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)(103,130)(104,132)(105,131)(106,127)
(107,129)(108,128)(109,133)(110,135)(111,134)(112,136)(113,138)(114,137)
(115,142)(116,144)(117,143)(118,139)(119,141)(120,140)(145,181)(146,183)
(147,182)(148,184)(149,186)(150,185)(151,190)(152,192)(153,191)(154,187)
(155,189)(156,188)(157,169)(158,171)(159,170)(160,172)(161,174)(162,173)
(163,178)(164,180)(165,179)(166,175)(167,177)(168,176);;
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*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 ];;
poly := F / rels;;

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

```
References : None.
to this polytope