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

You are not logged in.

## #1 Re: Help Me ! » dihedral angle confusion???? » 2011-08-29 02:50:12

bob,

subtracting from 90 because this is the "default" setting for the saw blade. (both table saw and band saw; 90 degrees = straight cut).

## #2 Re: Help Me ! » dihedral angle confusion???? » 2011-08-28 06:21:39

the required angles?

## #3 Help Me ! » dihedral angle confusion???? » 2011-08-28 06:02:22

jesseherring
Replies: 3

Wondering if anyone can explain/confirm my understanding of dihedral angles relating to woodworking.  as an example, if we are talking about a truncated icosahedron, the published dihedral angles are:
hexagon-hexagon face: 138.1896851
hexagon-pentagon face: 142.6226319

Now these are the face to face angles for each of the two required polygons making up the faces of the truncated icosahedron.  If I want to construct a wooden model with 20 hexagons and 12 pentagons made of square sticks, how do I find the required bevels on the hexagons and pentagons? (see attached figures)  After a LOT of confusion I think this is one way to do so.
First, take the hexagon-hexagon face and divide in half which gives 69.09....  then subtract this from 90 to get the required bevel angle on the hex-hex sides of each hexagon.  This will be 20.9.....
Doing the same for the hexagon-pentagon faces gives a bevel of 18.68.....

thanks

## #4 Help Me ! » calculating dodecadodecahedron face angles » 2011-08-18 04:25:37

jesseherring
Replies: 1

Wondering if anybody could show me how to calculate the face angles of the dodecahedron.  I recently got a copy of Mathematical Models and it has a table with some of the face angles calculated.  However it does not show how they got the angles.  Also does anybody know what a re-entrant angle is?

## #5 Re: Help Me ! » complex polyhedron models » 2011-07-29 15:59:11

mathisfun

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

## #6 Re: Help Me ! » complex polyhedron models » 2011-07-29 02:39:07

bob

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

jesse

## #7 Re: Help Me ! » complex polyhedron models » 2011-07-29 02:38:02

MathIsFun

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

jesse

## #8 Re: Help Me ! » complex polyhedron models » 2011-07-28 16:06:35

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.

## #9 Re: Help Me ! » complex polyhedron models » 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.

## #10 Re: Help Me ! » complex polyhedron models » 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?

## #11 Re: Help Me ! » complex polyhedron models » 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?)

another diagram

## #13 Re: Help Me ! » complex polyhedron models » 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

## #14 Re: Help Me ! » complex polyhedron models » 2011-07-28 05:09:20

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

## #15 Re: Help Me ! » complex polyhedron models » 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

## #16 Re: Help Me ! » complex polyhedron models » 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."

## #17 Re: Help Me ! » complex polyhedron models » 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.

## #18 Re: Help Me ! » complex polyhedron models » 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.

## #19 Help Me ! » complex polyhedron models » 2011-07-27 07:07:52

jesseherring
Replies: 43

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