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bob,

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

the required angles?

**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.....

Is this the correct method to find these angles? PLEASE HELP!!!

thanks

**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?

mathisfun

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

bob

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

jesse

MathIsFun

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

jesse

bobby,

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

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

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

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

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

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

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."

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.

**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

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