... In my prefabricated conceptual cosmic heirarchy yes the Pen-Dod. would be inside the Ico. Cube inside of Oct. Does the geometry of equal unitary edged...
... should ... Alan, this does not inlcude the most volume for same length of edged, Rhombic Dodecahedron. http://en.wikipedia.org/wiki/Rhombic_dodecahedron ...
Hi Rybo ... I don't follow. A unit edged pentagonal dodecahedron has more than twice the volume of a unit edged rhombic dodecahedron. Adrian. -- Adrian...
Hi Alan ... It depends on what you mean. The "extra" contact is edge-to-edge contact, rather than vertex-to-edge contact. However, where the tetrahedron...
... Adrian, you are correct on this one, but please see my critique on http://groups.yahoo.com/group/synergeo/message/15049 I adjusted the lengths of the edges...
Hi Guys This has been a fascinating discourse over the last few days and I've been meaning to chyme in. I would love to prepare some aids to illustrate some of...
One thing I forgot to mention is if one scales the 2nd rotated tetra by 3 or 0.3333 then they get the actual tetrahedron self dual where the vertices of one...
Ok thanks Allan, you already have it. I figured you guys new this, but I'm just finding it out by myself. Its related to the Insphere/Circumsphere ratio of...
... but ... I think that it has something to do with the SQRT(3). After all, in our three-dimensional world, the diagonal of the cube is SQRT(1+1+1) times the...
Hi Alan ... It may be a bit difficult to pick out the individual polyhedra in my model as the triangle faced polyhedra all have the same colour struts. What I...
I should have read through a bit further. Here is the relationship stated, hopefully, a bit more clearly... Take each face of an icosahedron and divide its...
... and also face-to-face (in case it adds confusion if I don't mention it). Adrian. -- Adrian Rossiter adrian@... Home: http://antiprism.com/adrian...
Hi Craig ... The circumcentre of a regular tetrahedron is also its centroid. The centroid of a right regular pyramid lies 1/4 of its height above its base. ...
The centroid of =any= homogeneous solid pyramid or cone lies at 1/4 of its height above its basis plane. It lies at 1/4 of the line segment from the centroid...
the [3-fold] apexes of the tetrahedra that are in the same positions as … the [3-fold] vertices of the cube (hexahedron) that are in the same positions as...
... The 3-valent VERTICES of the stella octangula make contact with the 3-valent triangle faces of the octahedron or icosahedron. The 3-valent FACES of the...
Could you tell me if you know of any Visual Basic related code snippets available online for creating models of geometric shapes, solids and rotating them? ......
Hi Adrian OK, I think I get it now Since Allan did mentioned that the 3D diagonal of the 1x1x1 cube is sqrt(3), which is why the Strut Length of the Pyramid...
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the Polytopia group. File : /Craig's...
Polytopia@yahoogroups...
Nov 4, 2006 2:35 pm
1379
Hi y'all This is perhaps my favourite combination of polyhedrons. An Octahedron inside a Stella Octangula inside a Rhombic Dodecahedron showing the coincident...
Hi Craig ... If you are talking about something calculated by software, then it will be the centre of a box that contains the vertices of the shape. If you...
... Now put the cursor on the image in the MIDDLE, and you will see the octahedron "grow" to a rhombic dodecahedron "grow" into a stella octangula! If you...
... I think that he's talking about the "concave rhombic dodecahedron" that's formed by the cube's diagonals. ... The box bounds the half of the cube that...
Having problems with message search?
Fill out this form to ensure your group is one of the first to be migrated to the new message search system.
