Math Is Fun Forum

jesseherring

Member

Registered: 2011-07-26

Posts: 19

Re: complex polyhedron models

is there any way to email or message certain members?  there is a post from a few years ago and i think the guy that created the thread could help me out if i could get a hold of him.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: complex polyhedron models

Hi jesseherring;

I can not do that. A members information is private. You might try contacting the Administrator, MathsIsFun. That is the best I can do, I am sorry.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: complex polyhedron models

hi jesseherring

I had to go back to the Wiki page to look up the coordinates for the calculation and there the answer is, sitting just left of the co-ordinates.  If you want is the angle between two planes, it is called the dihedral angle and for your solid it is 142.62 degrees.

General table at

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

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: complex polyhedron models

I recall helping him and making a dihedral angle calculator

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: complex polyhedron models

hi jessehherring

Ok. Here's the complete vector approach.

(i) I used the coordinates from the Wiki page and worked out which points are which on the diagram.  Below I have the icosadodecahedron and part of my spreadsheet for determining the coordinates.

(ii)  then I made my formula.  See the middle diagram

Suppose AHG is one triangle and AHJZX is one pentagon.  Let 'E' be the midpoint of AH. (note this E is not the coordinate labelled E in my sheet.  I was running short of letters!)

The angle between EG and EZ is the required dihedral angle.

I used the 'dot product' formula for calculating an angle between two vectors.

Top line is the dot product between the vectors.  Bottom is the product of their lengths.

These calculations are also shown on the sheet along with a conversion into degrees.

Bob

Last edited by Bob (2011-07-29 01:58:24)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

jesseherring

Member

Registered: 2011-07-26

Posts: 19

Re: complex polyhedron models

MathIsFun

   wondering if it would be possible to somehow get a message to SoapyJoe regarding his adventures with similar problem?

jesse

jesseherring

Member

Registered: 2011-07-26

Posts: 19

Re: complex polyhedron models

bob

   i need to sit down and take a good look at this, i cannot thank you enough for your help

jesse

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: complex polyhedron models

hi jesseherring,

You're welcome; it's been interesting to explore this.  Post back if you want anything clarified. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: complex polyhedron models

I sent an email about this to "Soapy Joe", hopefully it will reach him.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

jesseherring

Member

Registered: 2011-07-26

Posts: 19

Re: complex polyhedron models

mathisfun

   thank you i appreciate it, i will keep my fingers crossed

SoapyJoe

Member

Registered: 2006-05-19

Posts: 71

Re: complex polyhedron models

Hi

Been quite a while since I last looked at this forum...

I have made a dozen or so wood models ...

How do I post pictures to this forum?

Would Jesseherring contact me direct at [hidden]

Soapy

Last edited by MathsIsFun (2011-07-30 12:30:52)

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: complex polyhedron models

Hi Joe, I sent your email to Jesse, so hiding it now

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

ballman

Member

Registered: 2011-07-31

Posts: 1

Re: 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

I suggest that you purchase the 'MAHEMATICAL MODELS' book by H.Martyn Cundy and
  A.P.Rollett  go to the inter-net and find a second hand version. Less than $20. ( 1961 )

If you are so inclined, you can learn about Miller Indices, vector analysis, and analytical
geometry.   If you are well versed in those subjects, then you can generate your own angles.

I have been making models since  1960 and have a truncated hexacontrahedron in the mathematics archives of the Smithsonian Institute.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: complex polyhedron models

I used the coordinates from the Wiki page and worked out which points are which on the diagram.  Below I have the icosadodecahedron and part of my spreadsheet for determining the coordinates.

Now, how did the wiki work out the co-ordinates without knowing the dihedral angles?

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: complex polyhedron models

hi Agnishom,

Good question.  I don't know how a person could work them out from scratch.  But you can test that they are correct like this:

Draw and label a Schlegel diagram for the solid.

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

Take pairs of points, using the co-ordinates, and find the distance between them.  (Best on a spreadsheet with a distance formula)

When you find a pair that are the minimum distance apart they must be adjacent on the Schlegel diagram, so pick a suitable pair of letters and assign them to the co-ordinates.  Keep doing this until you have labelled them all.

Then you can choose points for two adjacent faces and do the cosine rule trick.  That's basically what I did for post 30.  If you look carefully at my screen shot of the spreadsheet, you'll see I have shrunk some columns.  That has hidden all my distance apart calculations.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: complex polyhedron models

Take pairs of points, using the co-ordinates, and find the distance between them.

How???
Where do I get them from??

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: complex polyhedron models

hi Agnishom,

Go to

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

Section titled "Cartesian Co-ordinates"

The diagram shows which points are which,  so that should make the task a lot easier.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: complex polyhedron models

The Wikipedia gives the following formula regarding dihedral angles,
Let p = The number of edges at each face
and q = The number of faces meeting at each vertex
and θ the dihedral angle.
Now,

Last edited by Agnishom (2013-01-15 14:50:51)

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: complex polyhedron models

hi Agnishom,

Thanks.  I'd not met that before.  I wonder how it is derived.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob