complex polyhedron models

jesseherring · 2011-07-27 07:07:52

Can anyone help me or point me in the right direction to find the angles needed in order to build a wood model of an icosidodecahedron, truncated icosahedron, and/or the 3V form of an icosahedron. I found Soapy Joes posting on the subject and could not gather how to figure out the angles from his discussions. I would like to be able to derive the angles so that I can later construct the rest of da vincis polyhedra.

thanks
Jesse

anonimnystefy · 2011-07-27 07:15:05

hi jesseherring

welcome to the forum.
is the icosidodecahedron going to be regular?why are you building it.

Bob · 2011-07-27 10:10:33

hi jesseherring

Check this page

http://en.wikipedia.org/wiki/Icosidodecahedron

Is that what you want?

This page gives the co-ordinates of the vertices. So a bit of 3-D vector geometry should give the angles.

Post back to confirm the solid and that'll give me time to work out a suitable vector equation. (It's kinda late here in the UK so I need to sleep on it.

Bob

Last edited by Bob (2011-07-27 10:11:37)

jesseherring · 2011-07-27 15:44:40

after seeing george harts website and finding da vinci's polyhedra drawings, I have become obsessed with trying to figure out how to build one for myself. I figured out how to construct an intersecting 5 tetrahedra model with help on a timber framers forum, however I still cannot make sense of how they derive the angles needed. (I do have a BS in Computer Science, but even with this background all of the abbreviations and the way they find the necessary angles make no sense to me?) I would like begin by making a model of the elevated icosidodecahedron as shown in the drawing by da vinci. sorry about giving you the wrong name bob.

bobbym · 2011-07-27 17:56:36

Hi;

Instead of dealing with the whole problem at once why not just post where you are right now? What particular calculation is giving you trouble. What have you got so far?

jesseherring · 2011-07-28 03:10:48

bobby hi,

I need to start from the very beginning. Hopefully after someone can walk me through the procedure for this model I will then be able to tackle any polyhedra on my own. So I guess to start with I need to figure out the angles need for the regular icosidodecahedron.

anonimnystefy · 2011-07-28 03:15:01

you should just figure out what the angles are in a regular pentagon and a equilateral triangle.

Last edited by anonimnystefy (2011-07-28 03:17:26)

bobbym · 2011-07-28 03:18:34

Hi all;

Are we talking about the same things?

http://en.wikipedia.org/wiki/Icosidodecahedron

Is that the object?

anonimnystefy · 2011-07-28 03:22:06

maybe and maybe not.

as i can see on the picture the icosidodecahedron consists of pentagons and triangles.

Last edited by anonimnystefy (2011-07-28 03:22:51)

jesseherring · 2011-07-28 03:43:31

bobby hello again,

yes i believe that it is the core of the elevated icosidodecahedron. from another site - "It is a nonconvex construction of 120 equilateral triangles arranged with icosahedral symmetry. Three-sided and five-sided pyramids have been erected on the faces of the underlying icosidodecahedron, which consists of twenty triangles and twelve pentagons."

bobbym · 2011-07-28 03:46:16

Hi jesseherring;

I remember this question, I also remember no one resolved it.

It looks very complicated.

anonimnystefy · 2011-07-28 03:46:17

hi jesseherring

i found this somewhere.http://www.rwgrayprojects.com/Lynn/NCH/whatpoly.html

were you thinking of that polyhedron?

jesseherring · 2011-07-28 04:00:06

bobby

i could not find any threads that were on this topic. maybe i was searching using the wrong keywords?

anonimnystefy, i do not think its the same thing

bobbym · 2011-07-28 04:04:30

Where would you start? I mean for the construction of the thing. How large is it to be?

jesseherring · 2011-07-28 05:09:20

to be able to safely cut all the pieces i would say 14-18 inches

bobbym · 2011-07-28 05:16:07

Hi;

Have you seen this?

http://www.worksheetworks.com/math/geom … edron.html

jesseherring · 2011-07-28 05:29:51

wondering if anyone could explain these diagrams to me. if i understand how these work i believe that i may be able to eventually figure out the needed angles for the icosidodecahedron.

jesse

jesseherring · 2011-07-28 05:31:28

another diagram

bobbym · 2011-07-28 05:38:57

What I meant that from post #16 you could actually build one out of stiff cardboard or say sheet metal. They are providing the template. We used to construct fairly large and perfect pyramids with the same idea.

jesseherring · 2011-07-28 05:41:58

bobby

thats my next step i guess is to build a model using a template. the diagrams that i posted were used to find angles for a 3V form of the icosahedron. (from vertices i guess?)

bobbym · 2011-07-28 05:46:51

thats my next step i guess is to build a model using a template.

Sometimes calculating is out and you are left with measurements. In the old days Galileo and Kepler solved tough math problems by weighing things. They were actually able to determine centers of gravity and areas under curves.

That page has printed out for a template that I downloaded. Take that template and blow it up with a good printer.

find angles for a 3V form of the icosahedron

An icosahedron is not the same shape. What is learned by doing that may not carry over to the real problem.

jesseherring · 2011-07-28 05:57:41

do you know how to solve for angles using 3d vector geometry as described in #3 using the vertices?

bobbym · 2011-07-28 06:04:57

Maybe! If I can not someone else can. First I would construct a model, either in reality or in a computer. A 3D model, those 2D drawings do not provide me with enough insight.

Your first post says you want to build it. Can you really measure out an angle of 7 degrees 11 minutes and 31 seconds? If you know the angles what good does that do towards building it? I mean do you really require the precision that calculation gives to construct it? You will have to approximate those angles in your construction.

So the question is are you building it or mathematically describing it?

jesseherring · 2011-07-28 15:34:33

bobby,

i am trying to build it. i have printed out a template and i will get it glued together tomorrow morning.

bobbym · 2011-07-28 15:43:39

Hi;

Let me know how you do. If you decide to make it our of stiff cardboard we used to half score ( cut through ) the line with an exacto knife. That allows the edges to bend but still stay together. This makes a somewhat stronger figure than paper.

Math Is Fun Forum

#1 2011-07-27 07:07:52

complex polyhedron models

#2 2011-07-27 07:15:05

Re: complex polyhedron models

#3 2011-07-27 10:10:33

Re: complex polyhedron models

#4 2011-07-27 15:44:40

Re: complex polyhedron models

#5 2011-07-27 17:56:36

Re: complex polyhedron models

#6 2011-07-28 03:10:48

Re: complex polyhedron models

#7 2011-07-28 03:15:01

Re: complex polyhedron models

#8 2011-07-28 03:18:34

Re: complex polyhedron models

#9 2011-07-28 03:22:06

Re: complex polyhedron models

#10 2011-07-28 03:43:31

Re: complex polyhedron models

#11 2011-07-28 03:46:16

Re: complex polyhedron models

#12 2011-07-28 03:46:17

Re: complex polyhedron models

#13 2011-07-28 04:00:06

Re: complex polyhedron models

#14 2011-07-28 04:04:30

Re: complex polyhedron models

#15 2011-07-28 05:09:20

Re: complex polyhedron models

#16 2011-07-28 05:16:07

Re: complex polyhedron models

#17 2011-07-28 05:29:51

Re: complex polyhedron models

#18 2011-07-28 05:31:28

Re: complex polyhedron models

#19 2011-07-28 05:38:57

Re: complex polyhedron models

#20 2011-07-28 05:41:58

Re: complex polyhedron models

#21 2011-07-28 05:46:51

Re: complex polyhedron models

#22 2011-07-28 05:57:41

Re: complex polyhedron models

#23 2011-07-28 06:04:57

Re: complex polyhedron models

#24 2011-07-28 15:34:33

Re: complex polyhedron models

#25 2011-07-28 15:43:39

Re: complex polyhedron models

Board footer