Overview
- Group
- SmallGroup(6,1)
- Rank
- 2
- Schläfli Type
- {3}
- Vertices, edges, …
- 3, 3
- Order of s0s1
- 3
- Also known as
- triangle, 2-simplex, {3}. if this polytope has another name.
Special Properties
- Universal
- Spherical
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
8-fold
9-fold
10-fold
11-fold
12-fold
13-fold
14-fold
15-fold
16-fold
17-fold
18-fold
19-fold
20-fold
21-fold
22-fold
23-fold
24-fold
25-fold
26-fold
27-fold
28-fold
29-fold
30-fold
31-fold
32-fold
33-fold
34-fold
35-fold
36-fold
37-fold
38-fold
39-fold
40-fold
41-fold
42-fold
43-fold
44-fold
45-fold
46-fold
47-fold
48-fold
49-fold
50-fold
51-fold
52-fold
53-fold
54-fold
55-fold
56-fold
57-fold
58-fold
59-fold
60-fold
61-fold
62-fold
63-fold
64-fold
65-fold
66-fold
67-fold
68-fold
69-fold
70-fold
71-fold
72-fold
73-fold
74-fold
75-fold
76-fold
77-fold
78-fold
79-fold
80-fold
81-fold
82-fold
83-fold
84-fold
85-fold
86-fold
87-fold
88-fold
89-fold
90-fold
91-fold
92-fold
93-fold
94-fold
95-fold
96-fold
97-fold
98-fold
99-fold
100-fold
101-fold
102-fold
103-fold
104-fold
105-fold
106-fold
107-fold
108-fold
109-fold
110-fold
111-fold
112-fold
113-fold
114-fold
115-fold
116-fold
117-fold
118-fold
119-fold
120-fold
121-fold
122-fold
123-fold
124-fold
125-fold
126-fold
127-fold
128-fold
129-fold
130-fold
131-fold
132-fold
133-fold
134-fold
135-fold
136-fold
137-fold
138-fold
139-fold
140-fold
141-fold
142-fold
143-fold
144-fold
145-fold
146-fold
147-fold
148-fold
149-fold
150-fold
151-fold
152-fold
153-fold
154-fold
155-fold
156-fold
157-fold
158-fold
159-fold
160-fold
161-fold
162-fold
163-fold
164-fold
165-fold
166-fold
167-fold
168-fold
169-fold
170-fold
171-fold
172-fold
173-fold
174-fold
175-fold
176-fold
177-fold
178-fold
179-fold
180-fold
181-fold
182-fold
183-fold
184-fold
185-fold
186-fold
187-fold
188-fold
189-fold
190-fold
191-fold
192-fold
193-fold
194-fold
195-fold
196-fold
197-fold
198-fold
199-fold
200-fold
201-fold
202-fold
203-fold
204-fold
205-fold
206-fold
207-fold
208-fold
209-fold
210-fold
211-fold
212-fold
213-fold
214-fold
215-fold
216-fold
217-fold
218-fold
219-fold
220-fold
221-fold
222-fold
223-fold
224-fold
225-fold
226-fold
227-fold
228-fold
229-fold
230-fold
231-fold
232-fold
233-fold
234-fold
235-fold
236-fold
237-fold
238-fold
239-fold
240-fold
241-fold
242-fold
243-fold
244-fold
245-fold
246-fold
247-fold
248-fold
249-fold
250-fold
251-fold
252-fold
253-fold
254-fold
255-fold
257-fold
258-fold
259-fold
260-fold
261-fold
262-fold
263-fold
264-fold
265-fold
266-fold
267-fold
268-fold
269-fold
270-fold
271-fold
272-fold
273-fold
274-fold
275-fold
276-fold
277-fold
278-fold
279-fold
280-fold
281-fold
282-fold
283-fold
284-fold
285-fold
286-fold
287-fold
288-fold
289-fold
290-fold
291-fold
292-fold
293-fold
294-fold
295-fold
296-fold
297-fold
298-fold
299-fold
300-fold
301-fold
302-fold
303-fold
304-fold
305-fold
306-fold
307-fold
308-fold
309-fold
310-fold
311-fold
312-fold
313-fold
314-fold
315-fold
316-fold
317-fold
318-fold
319-fold
320-fold
321-fold
322-fold
323-fold
324-fold
325-fold
326-fold
327-fold
328-fold
329-fold
330-fold
331-fold
332-fold
333-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
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.