Questions?
See the FAQ
or other info.

# Polytope of Type {3}

Atlas Canonical Name : {3}*6
Also Known As : triangle, 2-simplex, {3}. if this polytope has another name.
Group : SmallGroup(6,1)
Rank : 2
Schlafli Type : {3}
Number of vertices, edges, etc : 3, 3
Order of s0s1 : 3
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2} of size 12
{3,3} of size 24
{3,4} of size 24
{3,6} of size 36
{3,4} of size 48
{3,6} of size 48
{3,5} of size 60
{3,8} of size 96
{3,12} of size 96
{3,6} of size 108
{3,5} of size 120
{3,10} of size 120
{3,10} of size 120
{3,6} of size 144
{3,12} of size 144
{3,6} of size 192
{3,8} of size 192
{3,10} of size 240
{3,12} of size 288
{3,24} of size 288
{3,6} of size 300
{3,10} of size 300
{3,6} of size 324
{3,18} of size 324
{3,7} of size 336
{3,8} of size 336
{3,8} of size 336
{3,10} of size 360
{3,15} of size 360
{3,8} of size 384
{3,12} of size 384
{3,6} of size 432
{3,12} of size 432
{3,20} of size 480
{3,7} of size 504
{3,9} of size 504
{3,6} of size 576
{3,24} of size 576
{3,12} of size 576
{3,6} of size 588
{3,14} of size 588
{3,9} of size 648
{3,12} of size 648
{3,8} of size 672
{3,8} of size 672
{3,14} of size 672
{3,8} of size 720
{3,10} of size 720
{3,10} of size 720
{3,30} of size 720
{3,16} of size 768
{3,24} of size 768
{3,6} of size 768
{3,16} of size 768
{3,12} of size 864
{3,24} of size 864
{3,6} of size 900
{3,30} of size 900
{3,18} of size 972
{3,6} of size 972
{3,18} of size 972
{3,7} of size 1008
{3,9} of size 1008
{3,14} of size 1008
{3,14} of size 1008
{3,18} of size 1008
{3,18} of size 1008
{3,8} of size 1008
{3,21} of size 1008
{3,7} of size 1092
{3,13} of size 1092
{3,12} of size 1152
{3,24} of size 1152
{3,12} of size 1152
{3,24} of size 1152
{3,24} of size 1152
{3,6} of size 1200
{3,20} of size 1200
{3,6} of size 1296
{3,36} of size 1296
{3,12} of size 1296
{3,18} of size 1296
{3,12} of size 1296
{3,18} of size 1296
{3,10} of size 1320
{3,10} of size 1320
{3,11} of size 1320
{3,12} of size 1320
{3,12} of size 1320
{3,16} of size 1344
{3,16} of size 1344
{3,28} of size 1344
{3,20} of size 1440
{3,60} of size 1440
{3,8} of size 1440
{3,10} of size 1440
{3,15} of size 1440
{3,20} of size 1440
{3,6} of size 1452
{3,22} of size 1452
{3,10} of size 1500
{3,30} of size 1500
{3,6} of size 1728
{3,24} of size 1728
{3,12} of size 1728
{3,6} of size 1764
{3,42} of size 1764
Vertex Figure Of :
{2,3} of size 12
{3,3} of size 24
{4,3} of size 24
{6,3} of size 36
{4,3} of size 48
{6,3} of size 48
{5,3} of size 60
{8,3} of size 96
{12,3} of size 96
{6,3} of size 108
{5,3} of size 120
{10,3} of size 120
{10,3} of size 120
{6,3} of size 144
{12,3} of size 144
{6,3} of size 192
{8,3} of size 192
{10,3} of size 240
{12,3} of size 288
{24,3} of size 288
{6,3} of size 300
{10,3} of size 300
{6,3} of size 324
{18,3} of size 324
{7,3} of size 336
{8,3} of size 336
{8,3} of size 336
{10,3} of size 360
{15,3} of size 360
{8,3} of size 384
{12,3} of size 384
{6,3} of size 432
{12,3} of size 432
{20,3} of size 480
{7,3} of size 504
{9,3} of size 504
{6,3} of size 576
{24,3} of size 576
{12,3} of size 576
{6,3} of size 588
{14,3} of size 588
{9,3} of size 648
{12,3} of size 648
{8,3} of size 672
{8,3} of size 672
{14,3} of size 672
{8,3} of size 720
{10,3} of size 720
{10,3} of size 720
{30,3} of size 720
{16,3} of size 768
{24,3} of size 768
{6,3} of size 768
{16,3} of size 768
{12,3} of size 864
{24,3} of size 864
{6,3} of size 900
{30,3} of size 900
{18,3} of size 972
{6,3} of size 972
{18,3} of size 972
{7,3} of size 1008
{9,3} of size 1008
{14,3} of size 1008
{14,3} of size 1008
{18,3} of size 1008
{18,3} of size 1008
{8,3} of size 1008
{21,3} of size 1008
{7,3} of size 1092
{13,3} of size 1092
{12,3} of size 1152
{24,3} of size 1152
{12,3} of size 1152
{24,3} of size 1152
{24,3} of size 1152
{6,3} of size 1200
{20,3} of size 1200
{6,3} of size 1296
{36,3} of size 1296
{12,3} of size 1296
{18,3} of size 1296
{12,3} of size 1296
{18,3} of size 1296
{10,3} of size 1320
{10,3} of size 1320
{11,3} of size 1320
{12,3} of size 1320
{12,3} of size 1320
{16,3} of size 1344
{16,3} of size 1344
{28,3} of size 1344
{20,3} of size 1440
{60,3} of size 1440
{8,3} of size 1440
{10,3} of size 1440
{15,3} of size 1440
{20,3} of size 1440
{6,3} of size 1452
{22,3} of size 1452
{10,3} of size 1500
{30,3} of size 1500
{6,3} of size 1728
{24,3} of size 1728
{12,3} of size 1728
{6,3} of size 1764
{42,3} of size 1764
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {6}*12
3-fold covers : {9}*18
4-fold covers : {12}*24
5-fold covers : {15}*30
6-fold covers : {18}*36
7-fold covers : {21}*42
8-fold covers : {24}*48
9-fold covers : {27}*54
10-fold covers : {30}*60
11-fold covers : {33}*66
12-fold covers : {36}*72
13-fold covers : {39}*78
14-fold covers : {42}*84
15-fold covers : {45}*90
16-fold covers : {48}*96
17-fold covers : {51}*102
18-fold covers : {54}*108
19-fold covers : {57}*114
20-fold covers : {60}*120
21-fold covers : {63}*126
22-fold covers : {66}*132
23-fold covers : {69}*138
24-fold covers : {72}*144
25-fold covers : {75}*150
26-fold covers : {78}*156
27-fold covers : {81}*162
28-fold covers : {84}*168
29-fold covers : {87}*174
30-fold covers : {90}*180
31-fold covers : {93}*186
32-fold covers : {96}*192
33-fold covers : {99}*198
34-fold covers : {102}*204
35-fold covers : {105}*210
36-fold covers : {108}*216
37-fold covers : {111}*222
38-fold covers : {114}*228
39-fold covers : {117}*234
40-fold covers : {120}*240
41-fold covers : {123}*246
42-fold covers : {126}*252
43-fold covers : {129}*258
44-fold covers : {132}*264
45-fold covers : {135}*270
46-fold covers : {138}*276
47-fold covers : {141}*282
48-fold covers : {144}*288
49-fold covers : {147}*294
50-fold covers : {150}*300
51-fold covers : {153}*306
52-fold covers : {156}*312
53-fold covers : {159}*318
54-fold covers : {162}*324
55-fold covers : {165}*330
56-fold covers : {168}*336
57-fold covers : {171}*342
58-fold covers : {174}*348
59-fold covers : {177}*354
60-fold covers : {180}*360
61-fold covers : {183}*366
62-fold covers : {186}*372
63-fold covers : {189}*378
64-fold covers : {192}*384
65-fold covers : {195}*390
66-fold covers : {198}*396
67-fold covers : {201}*402
68-fold covers : {204}*408
69-fold covers : {207}*414
70-fold covers : {210}*420
71-fold covers : {213}*426
72-fold covers : {216}*432
73-fold covers : {219}*438
74-fold covers : {222}*444
75-fold covers : {225}*450
76-fold covers : {228}*456
77-fold covers : {231}*462
78-fold covers : {234}*468
79-fold covers : {237}*474
80-fold covers : {240}*480
81-fold covers : {243}*486
82-fold covers : {246}*492
83-fold covers : {249}*498
84-fold covers : {252}*504
85-fold covers : {255}*510
86-fold covers : {258}*516
87-fold covers : {261}*522
88-fold covers : {264}*528
89-fold covers : {267}*534
90-fold covers : {270}*540
91-fold covers : {273}*546
92-fold covers : {276}*552
93-fold covers : {279}*558
94-fold covers : {282}*564
95-fold covers : {285}*570
96-fold covers : {288}*576
97-fold covers : {291}*582
98-fold covers : {294}*588
99-fold covers : {297}*594
100-fold covers : {300}*600
101-fold covers : {303}*606
102-fold covers : {306}*612
103-fold covers : {309}*618
104-fold covers : {312}*624
105-fold covers : {315}*630
106-fold covers : {318}*636
107-fold covers : {321}*642
108-fold covers : {324}*648
109-fold covers : {327}*654
110-fold covers : {330}*660
111-fold covers : {333}*666
112-fold covers : {336}*672
113-fold covers : {339}*678
114-fold covers : {342}*684
115-fold covers : {345}*690
116-fold covers : {348}*696
117-fold covers : {351}*702
118-fold covers : {354}*708
119-fold covers : {357}*714
120-fold covers : {360}*720
121-fold covers : {363}*726
122-fold covers : {366}*732
123-fold covers : {369}*738
124-fold covers : {372}*744
125-fold covers : {375}*750
126-fold covers : {378}*756
127-fold covers : {381}*762
128-fold covers : {384}*768
129-fold covers : {387}*774
130-fold covers : {390}*780
131-fold covers : {393}*786
132-fold covers : {396}*792
133-fold covers : {399}*798
134-fold covers : {402}*804
135-fold covers : {405}*810
136-fold covers : {408}*816
137-fold covers : {411}*822
138-fold covers : {414}*828
139-fold covers : {417}*834
140-fold covers : {420}*840
141-fold covers : {423}*846
142-fold covers : {426}*852
143-fold covers : {429}*858
144-fold covers : {432}*864
145-fold covers : {435}*870
146-fold covers : {438}*876
147-fold covers : {441}*882
148-fold covers : {444}*888
149-fold covers : {447}*894
150-fold covers : {450}*900
151-fold covers : {453}*906
152-fold covers : {456}*912
153-fold covers : {459}*918
154-fold covers : {462}*924
155-fold covers : {465}*930
156-fold covers : {468}*936
157-fold covers : {471}*942
158-fold covers : {474}*948
159-fold covers : {477}*954
160-fold covers : {480}*960
161-fold covers : {483}*966
162-fold covers : {486}*972
163-fold covers : {489}*978
164-fold covers : {492}*984
165-fold covers : {495}*990
166-fold covers : {498}*996
167-fold covers : {501}*1002
168-fold covers : {504}*1008
169-fold covers : {507}*1014
170-fold covers : {510}*1020
171-fold covers : {513}*1026
172-fold covers : {516}*1032
173-fold covers : {519}*1038
174-fold covers : {522}*1044
175-fold covers : {525}*1050
176-fold covers : {528}*1056
177-fold covers : {531}*1062
178-fold covers : {534}*1068
179-fold covers : {537}*1074
180-fold covers : {540}*1080
181-fold covers : {543}*1086
182-fold covers : {546}*1092
183-fold covers : {549}*1098
184-fold covers : {552}*1104
185-fold covers : {555}*1110
186-fold covers : {558}*1116
187-fold covers : {561}*1122
188-fold covers : {564}*1128
189-fold covers : {567}*1134
190-fold covers : {570}*1140
191-fold covers : {573}*1146
192-fold covers : {576}*1152
193-fold covers : {579}*1158
194-fold covers : {582}*1164
195-fold covers : {585}*1170
196-fold covers : {588}*1176
197-fold covers : {591}*1182
198-fold covers : {594}*1188
199-fold covers : {597}*1194
200-fold covers : {600}*1200
201-fold covers : {603}*1206
202-fold covers : {606}*1212
203-fold covers : {609}*1218
204-fold covers : {612}*1224
205-fold covers : {615}*1230
206-fold covers : {618}*1236
207-fold covers : {621}*1242
208-fold covers : {624}*1248
209-fold covers : {627}*1254
210-fold covers : {630}*1260
211-fold covers : {633}*1266
212-fold covers : {636}*1272
213-fold covers : {639}*1278
214-fold covers : {642}*1284
215-fold covers : {645}*1290
216-fold covers : {648}*1296
217-fold covers : {651}*1302
218-fold covers : {654}*1308
219-fold covers : {657}*1314
220-fold covers : {660}*1320
221-fold covers : {663}*1326
222-fold covers : {666}*1332
223-fold covers : {669}*1338
224-fold covers : {672}*1344
225-fold covers : {675}*1350
226-fold covers : {678}*1356
227-fold covers : {681}*1362
228-fold covers : {684}*1368
229-fold covers : {687}*1374
230-fold covers : {690}*1380
231-fold covers : {693}*1386
232-fold covers : {696}*1392
233-fold covers : {699}*1398
234-fold covers : {702}*1404
235-fold covers : {705}*1410
236-fold covers : {708}*1416
237-fold covers : {711}*1422
238-fold covers : {714}*1428
239-fold covers : {717}*1434
240-fold covers : {720}*1440
241-fold covers : {723}*1446
242-fold covers : {726}*1452
243-fold covers : {729}*1458
244-fold covers : {732}*1464
245-fold covers : {735}*1470
246-fold covers : {738}*1476
247-fold covers : {741}*1482
248-fold covers : {744}*1488
249-fold covers : {747}*1494
250-fold covers : {750}*1500
251-fold covers : {753}*1506
252-fold covers : {756}*1512
253-fold covers : {759}*1518
254-fold covers : {762}*1524
255-fold covers : {765}*1530
257-fold covers : {771}*1542
258-fold covers : {774}*1548
259-fold covers : {777}*1554
260-fold covers : {780}*1560
261-fold covers : {783}*1566
262-fold covers : {786}*1572
263-fold covers : {789}*1578
264-fold covers : {792}*1584
265-fold covers : {795}*1590
266-fold covers : {798}*1596
267-fold covers : {801}*1602
268-fold covers : {804}*1608
269-fold covers : {807}*1614
270-fold covers : {810}*1620
271-fold covers : {813}*1626
272-fold covers : {816}*1632
273-fold covers : {819}*1638
274-fold covers : {822}*1644
275-fold covers : {825}*1650
276-fold covers : {828}*1656
277-fold covers : {831}*1662
278-fold covers : {834}*1668
279-fold covers : {837}*1674
280-fold covers : {840}*1680
281-fold covers : {843}*1686
282-fold covers : {846}*1692
283-fold covers : {849}*1698
284-fold covers : {852}*1704
285-fold covers : {855}*1710
286-fold covers : {858}*1716
287-fold covers : {861}*1722
288-fold covers : {864}*1728
289-fold covers : {867}*1734
290-fold covers : {870}*1740
291-fold covers : {873}*1746
292-fold covers : {876}*1752
293-fold covers : {879}*1758
294-fold covers : {882}*1764
295-fold covers : {885}*1770
296-fold covers : {888}*1776
297-fold covers : {891}*1782
298-fold covers : {894}*1788
299-fold covers : {897}*1794
300-fold covers : {900}*1800
301-fold covers : {903}*1806
302-fold covers : {906}*1812
303-fold covers : {909}*1818
304-fold covers : {912}*1824
305-fold covers : {915}*1830
306-fold covers : {918}*1836
307-fold covers : {921}*1842
308-fold covers : {924}*1848
309-fold covers : {927}*1854
310-fold covers : {930}*1860
311-fold covers : {933}*1866
312-fold covers : {936}*1872
313-fold covers : {939}*1878
314-fold covers : {942}*1884
315-fold covers : {945}*1890
316-fold covers : {948}*1896
317-fold covers : {951}*1902
318-fold covers : {954}*1908
319-fold covers : {957}*1914
320-fold covers : {960}*1920
321-fold covers : {963}*1926
322-fold covers : {966}*1932
323-fold covers : {969}*1938
324-fold covers : {972}*1944
325-fold covers : {975}*1950
326-fold covers : {978}*1956
327-fold covers : {981}*1962
328-fold covers : {984}*1968
329-fold covers : {987}*1974
330-fold covers : {990}*1980
331-fold covers : {993}*1986
332-fold covers : {996}*1992
333-fold covers : {999}*1998
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
poly := Group([s0,s1]);;

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

```
Permutation Representation (Magma) :
```s0 := Sym(3)!(2,3);
s1 := Sym(3)!(1,2);
poly := sub<Sym(3)|s0,s1>;

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

```
References : None.
to this polytope