tag:blogger.com,1999:blog-36269973.post6635235465535140092..comments2017-10-05T14:08:36.099-05:00Comments on The Mathematical Tourist: Hexagons, Pentagons, and Geodesic DomesMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-36269973.post-5290574069000512402017-01-12T16:06:31.605-05:002017-01-12T16:06:31.605-05:00I would like to build some models, first of a regu...I would like to build some models, first of a regular dome to gain familiarity<br />with domes and their structures. But second to build a prototype of a model<br />for a "nature-house", which is a greenhouse that encloses a house.<br /><br />As if that is not difficult enough, I would also like to find out if there are any<br />rules about scaling a dome and its measurements Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-36269973.post-17602878295625195492016-07-27T11:35:15.767-05:002016-07-27T11:35:15.767-05:00http://assets.inhabitat.com/wp-content/blogs.dir/1...http://assets.inhabitat.com/wp-content/blogs.dir/1/files/2012/02/Biosphere11.jpg<br /><br />this image shows at least one of the pentagons, on the left side of the image.Kailoss _https://www.blogger.com/profile/08269089333802899243noreply@blogger.comtag:blogger.com,1999:blog-36269973.post-88172870102699402082015-06-11T09:07:48.262-05:002015-06-11T09:07:48.262-05:00This is right in that there do not have to be pent...This is right in that there do not have to be pentagons, but is incorrect in that it is hexagon based. Regular hexagons of all the same size can only tile a plane, by basic Euclidean geometry. No curvature can ever be made from arranging only hexagons.<br />The Montreal dome is a frequency 16 icosahedron: equilateral triangle based. Each triangle of the regular icosahedron has been split into 16 Ronald Letthttps://www.blogger.com/profile/00566950035789527315noreply@blogger.comtag:blogger.com,1999:blog-36269973.post-5213204513014377422015-05-23T10:33:16.449-05:002015-05-23T10:33:16.449-05:00The reason you haven't found any pentagons is ...The reason you haven't found any pentagons is because there do NOT have to be pentagons and there are NONE to be found.<br /><br />The Montreal Dome is a hexagon based geodesic dome. It consists of two layers of hexes connected by members to make tetrahedra and these tetrahedra, being triangular elements, provide the necessary rigidity else the dome would not be stable.Robnoreply@blogger.comtag:blogger.com,1999:blog-36269973.post-85429051670219165492014-02-07T19:34:53.457-05:002014-02-07T19:34:53.457-05:00The Biosphere is the classic 'soccer ball'...The Biosphere is the classic 'soccer ball' ( icosahedron ) with twelve pentagons surrounded by hexagons.<br />Since it is not a full sphere there are only 6 of the normal 12 pentagons. There is one at the very top, and then 5 in a row around the top third of the Biosphere.<br /><br />Tricks I use to find the pentagons.<br />Remember that, these pentagons are overlapping with hexagons, so Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-36269973.post-25962177740351621212014-02-07T19:32:48.788-05:002014-02-07T19:32:48.788-05:00The Biosphere is the classic 'soccer ball'...The Biosphere is the classic 'soccer ball' ( icosahedron ) with twelve pentagons surrounded by hexagons.<br />Since it is not a full sphere there are only 6 of the normal 12 pentagons. There is one at the very top, and then 5 in a row around the top third of the Biosphere.<br /><br />Tricks I use to find the pentagons.<br />Remember that, these pentagons are overlapping with hexagons, so Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-36269973.post-20161196741546907122012-07-20T22:43:07.564-05:002012-07-20T22:43:07.564-05:00Greeting Sir,
I read your article with interest....Greeting Sir,<br /><br /><br />I read your article with interest. I manage to create the simple icosahedron with Sktechup. But what is the method I should used to create complex icosahedron like the one shown in Geode_V_3_1_duale.png?shawebhttps://www.blogger.com/profile/15925645803059475708noreply@blogger.comtag:blogger.com,1999:blog-36269973.post-14908612069099788872011-08-13T11:36:49.016-05:002011-08-13T11:36:49.016-05:00Or, could it be that some of the hexagons were alt...Or, could it be that some of the hexagons were altered to form a tighter line of latitude; or triangles were inserted to fill-up the gaps .... those triangles can be calculted to match sections of the hexagons. I have not seen it .. but whatever it is, it must be very smart.Lorihttps://www.blogger.com/profile/08843314858846026319noreply@blogger.comtag:blogger.com,1999:blog-36269973.post-89780804722887155902010-10-25T01:38:50.642-05:002010-10-25T01:38:50.642-05:00A very interesting article and I also found it dif...A very interesting article and I also found it difficult to locate the pentagons in larger geodesic domes until I stopped looking for them.<br />Now I look for the hexagons:<br />a. because there are more of them<br />b. where there are hexagons there must be a pentagon adjacent to the hexagons.<br />Have been designing and manufacturing geodesic domes for many years.kwicksethttp://www.kwickset.net/noreply@blogger.com