Math Is Fun Forum

SoapyJoe

Member

Registered: 2006-05-19

Posts: 71

Re: Stellation of Icosahedron

Wow..... that looks great!

Let me play around a little with these figures and I will get back to you.

Off the top of my head..... this, in practice, boils down to only three angles 7.8 degrees, 10.0 degrees and 10.37 degrees. (the difference between 10.36 and 10.38)

One possible method of testing these figures, fairly quickly, may be to make just one section in this manner and the remaining 19 'faces' from sheet MDF. The 'joint' will not be exactly correct but, I feel, at this point in time, it should be a good guide.

Making an Icosahedron from MDF sheet is quite an easy option and if I join the MDF faces together with dowels  then .... I hope that I can replace individual MDF solid faces with 4V format faces and, if things are looking good, gradually build the full 4V in this manner.

DO YOU THINK THIS METHODOLOGY WILL WORK?

Soapy

SoapyJoe

Member

Registered: 2006-05-19

Posts: 71

Re: Stellation of Icosahedron

My first attempt to input your angles into a sketch of the Icosahedron  has, I am afraid, rather landed onto rocky ground.

I feel O.K. about sides CDEF but a bit confused about A and B

Not quite sure if this scan is any use....

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Stellation of Icosahedron

Wowee!! Nice dihedral angle, plane equation, calculator!!!!!! I'll be learning from that!!  Thanks for making it!!!!
"MathisFun Advanced" -- just noticed that, that's true.

---

igloo myrtilles fourmis

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Stellation of Icosahedron

Sorry, Joe and John, I completely missed your responses. I just thought "Soapy must be about to start on that 4V thing", so I checked, and here are messages I haven't responded to!

Thanks for the positive comments, John.

Umm, Joe ... yeah ... I calculated all "inside" angles, but not the edge ones.

It is really tricky. Not so much the maths, but just figuring out which surface is alongside which. So I have two sets of triangles, each set with 16 triangles. Now the 1-2-3 trangle on set one, its point "2" is really point "3" on the other set, and then the 3-5-6 triangle, its point 3 is point 2 and the 6 is point 4 so it matches, no, wait a minute, isn't that the wrong side, in which case ... arrggghhh!

Anyway, if I have matched them up correctly then:

         1
       2   3
     4   5   6
   7   8   9  10
11  12  13  14  15

1-2 is 10.51°
2-4 is 10.49°

Pretty silly if that is right - 10½ degrees is the answer for both

---

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

SoapyJoe

Member

Registered: 2006-05-19

Posts: 71

Re: Stellation of Icosahedron

Thanks.

I did wonder if you had gone on holiday.... I have not started on this project yet ...... just gathering up information and bits and bobs.

I am actually very, very busy on another massive project ....I am writing my dissertation for an MA. (Indian Literature)

But I do like to clear my head by working on these wood working projects.

Soapy

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Stellation of Icosahedron

Gosh, we have some Inidan members, too! Ganesh for one (who is currently absent but will return).

---

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

BurtonSexton

Guest

Re: Stellation of Icosahedron

My brother-in-law is trying to construct a wooden icosahedron.  Would you mind sending your e-mail addy so that he can correspond with you?  Many thanks.

Burton