167:. Rather, the definition you prefer seems to have arisen only in the last few years, as a consequence of abstraction away from concrete space. Yes it may be applied to real convex figures, but the result runs contrary to the usual understanding, e.g. for the snub cube. We do at least agree that the abstract treatment is of significant value and needs to be properly explaine here, but I do think that the more long-standing and widely used definition should be given first. — Cheers,
46:
21:
213:
Ok, but I don't see the point of having an article for that definition of "chiral polytope", any more than I need to have a separate article for "red polytope": we have an article on the color red, and we have an article on poytopes, but there are no special properties of red polytopes that do not
154:
While I can sympathise with this as a point of view, I find the emphasis unusual. In forty years of reading about polyhedra I have found the definition, requiring only a lack of mirror symmetry, to be universal and have never before come across the idea that for example the snub cube is not chiral
139:
I disagree — I think the strict definition can apply in all cases, and is not particularly abstract (it applies perfectly well to convex polytopes in geometric spaces, not just abstract ones, it merely happens to be the case that there aren't any with this weird kind of symmetry until you get to
163:. It is also given the Mathworld page given in the external links. I find it hard to maintain the view that these are merely "some sources" or that their usage is not "strict", or that this article should differ in definition from that given at
106:
So - is there some specialist area of abstract mathematics that has its own incompatible definition of the term "chiral", or is the current content incorrect? Either way, it is not telling the full story.
228:
Agreed. But given that the article title is inclusive of it, I think it requires a brief mention. Since it is the broader and more widely-used definition, best to get it out of the way first. — Cheers,
155:(though Cromwell spells it "cheiral", and some authors such as Coxetere tend to prefer "enantiomorphic"). Indeed, on Knowledge itself we find this definition apparent in the pages you link to on
92:
The definition given here, requiring that a chiral figure must have a certain symmetry and that no finite polyhedron (3-polytope) can be chiral, flies in the face of many published works. Even
140:
higher dimensions). I will try writing to make this more clear and to reflect the fact that the term has been applied less strictly in some sources. —
52:
26:
199:
gives a shoe as an example of a chiral object. However I am aware that this is not helpful for the study of abstract polytopes. — Cheers,
96:, referenced in support of this definition, is clear that polyhedra such as the snub cube are said to be chiral, e.g.
219:
186:
145:
196:
164:
156:
181:
So your position is that e.g. every irregular polytope (having a trivial symmetry group) is also chiral? —
234:
204:
172:
130:
115:
57:
31:
215:
182:
141:
125:
I took a stab at what I think is going on. Feel free to revert/correct as necessary. — Cheers,
230:
200:
168:
126:
111:
101:
45:
20:
160:
93:
214:
follow immediately from the separate properties of redness and polytopes. —
97:
238:
223:
208:
190:
176:
149:
134:
119:
102:http://demonstrations.wolfram.com/ChiralPolyhedra/
55:, a project which is currently considered to be
8:
15:
98:http://mathworld.wolfram.com/Chiral.html
67:Knowledge:WikiProject Uniform Polytopes
17:
70:Template:WikiProject Uniform Polytopes
7:
51:This article is within the scope of
195:Yes, in exactly the same way that
14:
44:
19:
1:
239:19:00, 1 September 2012 (UTC)
224:18:38, 1 September 2012 (UTC)
209:18:35, 1 September 2012 (UTC)
191:18:32, 1 September 2012 (UTC)
177:18:30, 1 September 2012 (UTC)
150:15:53, 1 September 2012 (UTC)
135:13:01, 1 September 2012 (UTC)
120:12:28, 1 September 2012 (UTC)
53:WikiProject Uniform Polytopes
267:
73:Uniform Polytopes articles
39:
197:chirality (mathematics)
165:chirality (mathematics)
157:chirality (mathematics)
85:
84:
81:
80:
64:Uniform Polytopes
27:Uniform Polytopes
258:
75:
74:
71:
68:
65:
48:
41:
40:
35:
23:
16:
266:
265:
261:
260:
259:
257:
256:
255:
90:
72:
69:
66:
63:
62:
29:
12:
11:
5:
264:
262:
254:
253:
252:
251:
250:
249:
248:
247:
246:
245:
244:
243:
242:
241:
216:David Eppstein
183:David Eppstein
142:David Eppstein
89:
86:
83:
82:
79:
78:
76:
49:
37:
36:
24:
13:
10:
9:
6:
4:
3:
2:
263:
240:
236:
232:
227:
226:
225:
221:
217:
212:
211:
210:
206:
202:
198:
194:
193:
192:
188:
184:
180:
179:
178:
174:
170:
166:
162:
158:
153:
152:
151:
147:
143:
138:
137:
136:
132:
128:
124:
123:
122:
121:
117:
113:
108:
104:
103:
99:
95:
87:
77:
60:
59:
54:
50:
47:
43:
42:
38:
33:
28:
25:
22:
18:
109:
105:
91:
56:
231:Steelpillow
201:Steelpillow
169:Steelpillow
159:and on the
127:Steelpillow
112:Steelpillow
110:— Cheers,
88:Definition
161:snub cube
94:mathworld
58:inactive
32:inactive
235:Talk
220:talk
205:Talk
187:talk
173:Talk
146:talk
131:Talk
116:Talk
100:and
237:)
222:)
207:)
189:)
175:)
148:)
133:)
118:)
233:(
218:(
203:(
185:(
171:(
144:(
129:(
114:(
61:.
34:)
30:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.