March 24, 2012 - Regular Icosahedron - Grasshopper2024-03-28T19:21:13Zhttps://www.grasshopper3d.com/forum/topics/march-24-2012-regular-icosahedron?groupUrl=coffee-and-grasshopper&commentId=2985220%3AComment%3A562381&groupId=2985220%3AGroup%3A560791&feed=yes&xn_auth=noSo how do you then get from t…tag:www.grasshopper3d.com,2013-07-23:2985220:Comment:8898562013-07-23T03:57:31.318ZBruce Blundellhttps://www.grasshopper3d.com/profile/BruceBlundell
<p>So how do you then get from there into a solid?</p>
<p></p>
<p>And then my next question is can this be truncated prior to going to a solid?</p>
<p></p>
<p>regards</p>
<p>Bruce</p>
<p>So how do you then get from there into a solid?</p>
<p></p>
<p>And then my next question is can this be truncated prior to going to a solid?</p>
<p></p>
<p>regards</p>
<p>Bruce</p> just for closure 10 component…tag:www.grasshopper3d.com,2012-03-25:2985220:Comment:5631542012-03-25T21:08:36.657ZDanny Boyeshttps://www.grasshopper3d.com/profile/DannyBoyes
<p>just for closure 10 components and all lines are present and correct.</p>
<p>just for closure 10 components and all lines are present and correct.</p> Here's the shortest I could c…tag:www.grasshopper3d.com,2012-03-25:2985220:Comment:5627932012-03-25T12:56:38.116ZDaniel Pikerhttps://www.grasshopper3d.com/profile/DanielPiker
<p>Here's the shortest I could come up with</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768719177?profile=original" target="_self"><img src="http://storage.ning.com/topology/rest/1.0/file/get/2768719177?profile=original" width="524" class="align-full"/></a></p>
<p>a few more possible solutions here:</p>
<p>Here's the shortest I could come up with</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768719177?profile=original" target="_self"><img src="http://storage.ning.com/topology/rest/1.0/file/get/2768719177?profile=original" width="524" class="align-full"/></a></p>
<p>a few more possible solutions here:</p> impressive!tag:www.grasshopper3d.com,2012-03-25:2985220:Comment:5627882012-03-25T12:29:13.710ZDaniel Pikerhttps://www.grasshopper3d.com/profile/DanielPiker
<p>impressive!</p>
<p>impressive!</p> 7 components, no typed data o…tag:www.grasshopper3d.com,2012-03-25:2985220:Comment:5626932012-03-25T12:17:34.161ZDanny Boyeshttps://www.grasshopper3d.com/profile/DannyBoyes
<p>7 components, no typed data or sliders ... but there is a line missing</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768719100?profile=original" target="_self"><img src="http://storage.ning.com/topology/rest/1.0/file/get/2768719100?profile=original" width="581" class="align-full"/></a></p>
<p>7 components, no typed data or sliders ... but there is a line missing</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768719100?profile=original" target="_self"><img src="http://storage.ning.com/topology/rest/1.0/file/get/2768719100?profile=original" width="581" class="align-full"/></a></p> slider is counted ?tag:www.grasshopper3d.com,2012-03-25:2985220:Comment:5624842012-03-25T00:07:53.607ZMateusz Zwierzyckihttps://www.grasshopper3d.com/profile/MateuszZwierzycki
<p>slider is counted ?</p>
<p>slider is counted ?</p> Great to see the range of way…tag:www.grasshopper3d.com,2012-03-24:2985220:Comment:5626282012-03-24T23:59:30.136ZDaniel Pikerhttps://www.grasshopper3d.com/profile/DanielPiker
<p>Great to see the range of ways this is possible.</p>
<p>How about with less than 10 components ?...</p>
<p>Great to see the range of ways this is possible.</p>
<p>How about with less than 10 components ?...</p> Nice, but I think the point i…tag:www.grasshopper3d.com,2012-03-24:2985220:Comment:5624662012-03-24T21:11:52.901ZMichael Pryorhttps://www.grasshopper3d.com/profile/MikePryor
<p>Nice, but I think the point is not to explain it, or show the definition screenshot on here for people who still want to figure it out themselves, at least not until the deadline is up :) still great stuff. </p>
<p>Nice, but I think the point is not to explain it, or show the definition screenshot on here for people who still want to figure it out themselves, at least not until the deadline is up :) still great stuff. </p> My attempt at the second chal…tag:www.grasshopper3d.com,2012-03-24:2985220:Comment:5624542012-03-24T19:28:16.818ZLucas Epphttps://www.grasshopper3d.com/profile/LukeEpp
<p>My attempt at the second challenge - creating it with no referenced or typed inputs. Used a bit of maths to establish the ratios between the Icosahedral radius and the radius of the two inscribed Pentagons. The resulting Icosahedron is exact. Not a very elegant solution (and still needs an input of 5 for the number of sides of a pentagon!) but the closest I could get on a first attempt...</p>
<p>This Icosahedron is created using the radius of one of the internal Pentagons as a starting…</p>
<p>My attempt at the second challenge - creating it with no referenced or typed inputs. Used a bit of maths to establish the ratios between the Icosahedral radius and the radius of the two inscribed Pentagons. The resulting Icosahedron is exact. Not a very elegant solution (and still needs an input of 5 for the number of sides of a pentagon!) but the closest I could get on a first attempt...</p>
<p>This Icosahedron is created using the radius of one of the internal Pentagons as a starting point.<br/>Firstly, the ratio of the Icosahedral and Pentagonal radii must be:<br/>Ricos / Rpent = Golden Ratio - 1/2</p>
<p>For a regular Icosahedron the two Pentagons must be parallel and separated by their Radius.</p>
<p>Thus the top and bottom vertices must be a distance of<br/>Ricos - Rpent/2<br/>from the two Pentagons. Using the above ratios however this simplifies to<br/>Rpent x (Golden Ratio - 1).</p>
<p></p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768719181?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2768719181?profile=RESIZE_1024x1024" width="721" class="align-full"/></a></p> nice one, I believe its the f…tag:www.grasshopper3d.com,2012-03-24:2985220:Comment:5624492012-03-24T18:35:23.777ZMichael Pryorhttps://www.grasshopper3d.com/profile/MikePryor
<p>nice one, I believe its the first definition I have seen to use golden ratio.</p>
<p>nice one, I believe its the first definition I have seen to use golden ratio.</p>