Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

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

jesseherring
Member
Registered: 2011-07-26
Posts: 19

complex polyhedron models

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

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: complex polyhedron models

hi jesseherring

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


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,538

Re: complex polyhedron models

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.  sleep

Bob

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


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

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

jesseherring
Member
Registered: 2011-07-26
Posts: 19

Re: complex polyhedron models

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.

View Image: leonardo-id-elevatum.gif

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,885

Re: complex polyhedron models

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?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

jesseherring
Member
Registered: 2011-07-26
Posts: 19

Re: complex polyhedron models

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.

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: complex polyhedron models

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)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,885

Re: complex polyhedron models

Hi all;

Are we talking about the same things?

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

Is that the object?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: complex polyhedron models

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)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

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

jesseherring
Member
Registered: 2011-07-26
Posts: 19

Re: complex polyhedron models

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."

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,885

Re: complex polyhedron models

Hi jesseherring;

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

It looks very complicated.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: complex polyhedron models

hi jesseherring

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

were you thinking of that polyhedron?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

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

jesseherring
Member
Registered: 2011-07-26
Posts: 19

Re: complex polyhedron models

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,885

Re: complex polyhedron models

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


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

jesseherring
Member
Registered: 2011-07-26
Posts: 19

Re: complex polyhedron models

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,885

Re: complex polyhedron models


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

jesseherring
Member
Registered: 2011-07-26
Posts: 19

Re: complex polyhedron models

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

View Image: 3VIcosahedronDiagram01.jpg View Image: icosahedronAnglesDiagram.jpg

Offline

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

jesseherring
Member
Registered: 2011-07-26
Posts: 19

Re: complex polyhedron models

another diagram

View Image: 3VIcosahedron_anglesDiagram.jpg

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,885

Re: complex polyhedron models

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.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

jesseherring
Member
Registered: 2011-07-26
Posts: 19

Re: complex polyhedron models

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?)

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,885

Re: complex polyhedron models

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.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

jesseherring
Member
Registered: 2011-07-26
Posts: 19

Re: complex polyhedron models

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,885

Re: complex polyhedron models

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?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

jesseherring
Member
Registered: 2011-07-26
Posts: 19

Re: complex polyhedron models

bobby,

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,885

Re: complex polyhedron models

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.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

Board footer

Powered by FluxBB