2D Squished Out of 3D

[Rybo]

Squishing 3D field/pattern of Nodal Vertexial Events into 2D field/pattern of parallel planes i.e. sort of a side view of these polyhedra is something new for me to try out and see what, if any thoughts it inspires.

Cube has 8 corners/vertexes on 2 parrallel planes.

…… * * * * …….minor skew/slant/deformation as .... * * * * ........( square pattern )
……. * * * * ……........................................... ....* * * * ....( square pattern )

X Y and Z dimensions ---one corner of a cube--- has 1 vertexion and 3 terminal-end-points( nippions ) on 2 parallel planes and below is just one of four possible orientations but all amount to same thing a set of right angle( 90 degrees ) set

…… * ……………………… or …………* ………….
……* * * ………………… ……… * * * ……..

Tetrahedron has 4 vertexes on 2 parallel planes and 60 degreeness pattern instead of the XYZ 90 degreeness pattern above.

……. * …….
…. * * * …..( triangle pattern )

Octahedon has 6 vertexes on 3 parallel planes.

….… * ………
.. * * * * ………( square pattern )
….… * …..

Icosahedron has 12 vertexes on 4 parrallel planes.

…….… * ……
…. * * * * * ……….( pentagonal{ phi } pattern )
…. * * * * * ………( "" "" )
………. * ……………

Cubo-octahedron has 12 vertexes on 3 parrallel planes.

…... * * * ……..( triangle pattern )
… * * * * * * …( hexagonal pattern )
……. * * * ……( triangle pattern )


Pentagonal-dodecahedron aka regular dodecahedron has 20 vertexes on 4 parrallel planes.

… * * * * * ….( pentagonal pattern )
… * * * * * ….( "" "" )
…. * * * * * ….( "" "" )
… * * * * * …….( "" "" )

Rhombic dodeachedron has 14 vertexes on 3 parrallel planes.

…... * * * * …..( rhombic{ diamond } pattern )
…. * * * * * * …..
……. * * * * …….( rhombic{ diamond } pattern ).

Rybo

[mkirkpatrick]

Thanks for the new thread rybo,however I have not a clue what you are talking about!

regards michael.

[Rybo]

Thanks for the new thread rybo,however I have not a clue what you are talking about!regards michael.

"Squishing" is plural of the word squash. Here again the reader has to be careful of many definitions of a word ie. the word squash can be yellow or green vegatable my post has no references to any vegatable.

The 2nd labeling is the word "3D" and that means 3 dimensional and 3D in mathematics, geomtry physics and many sciences refers to X, Y and Z ala cartesian coordinates.

"field", like many words, can have many differrent definitions and I used a "/" mark to help associate it with the word "pattern". Patterned field used "asterisks" as vertexes.

"Vertexes"( plural ) is geometric term that came from a dude name Euler, who stated that two lines crossing/intersecting/meeting are called a vertex.

So my each of my "asterisks" reprenting a "vertex", except in the patterned field of X, Y Z because X Y and Z lines only meet at one vertex. The other ends are open and do not meet with any other lines, so these are terminal end points.

Point compose a line in mathematics. The end of a line that does not meet/cross another line terminates with an "end point". I use the word "nippion" to equate as "terminal end point" i.. there is no 2nd third or more lines meeting at the end-point of the line.

Ok, so I strayed off from helping you to understand what the words mean in this post.

If you can be more specific as to which words you do not understand I can better assist you in your attempts to understand Michael.


Most of the words are in the dictionary but I understand how tedious that can be. Rybo

[Rybo]

"Squishing" is plural of the word squash. Here again the reader has to be careful of many definitions of a word ie. the word squash can be yellow or green vegatable my post has no references to any vegatable."Vertexes"( plural ) is geometric term that came from a dude name Euler, who stated that two lines crossing/intersecting/meeting are called a vertex.

----Nodal/node = joint in biology or vertexial crossings in geometry or fix/crossing of coordinates in mapping or electronics triangulation of a EMRadiational signal, or intersection/crossing of streets, or hub/center where spokes of wheel intersect or people cross paths to socialize etc.... so, we also see that there are many differrent words that intersect, or have some level of commonality when going from science to another.---

[mkirkpatrick]

Thanks rybo,its not the words I dont understand its the mathamatics maths is a very weak subject for me in particular when letters are used to denote equasions,I cannot fathom it,talk about universal principles behind all phenomena then I am online so to speak,but academic stuff forget about it!


regards michael.

[Rybo]

Thanks rybo,its not the words I dont understand its the mathamatics maths is a very weak subject for me in particular when letters are used to denote equasions,I cannot fathom it,talk about universal principles behind all phenomena then I am online so to speak,but academic stuff forget about it! regards michael.

Hi Michael, there were no "equations" in my message nor was there any adding, subtracting, multiplication division, so, if there was some math in that post, I'm not clear what maths that would be. I think the biggest problem, is not having a visual to go with each polyhedron.

Geometry is a very visual branch of mathematics i.e. less conceptuall than some mathemactics that do require much more abstract equations. Geometry eventuall has to inlcude the more abstract trigonometry and spherical trig is very difficult aspect of geometry.

Visuals are very helpful with geometry but part of what I was doing was taking one aspect ----vertexial nodal points--- of the 3D geometry and presenting in a more simple way.

Linear parrallel planes are more simple and that is what I posted, but again, without the original polyhedron visuals, I do understand a loss of connection betweent the 3D and the 2D outlines.

Well, nobody can say I didn't try, and who knows who may find or discover something useful to them or others some day. Rybo

[AntonioLao]

The most advanced branch of abstract geomety is now known as topology. But the topology I'm using for a quantum theory of space-time does not extend three dimensions. In fact, this theory works well in one and two dimensions without incorporating brane theory of superstring. The topologies I used are Hopf topology (1D), Mobius topology (2D), and Klein topology (3D).