Re: New Dekanys in VRML

Hi Paul,

I've done new versions of the dekanies now, with actual numbers at the vertices.

You can also read the list of audio clips to make at head of the file.

Did them for the 3)5 and 2)5 dekanies, for 1,3,5,7,9 and 1,3,5,7,11
2)5 dekany:

http://members.nbci.com/_XMCM/tune_smithy/dekany/cdekany2_1_3_5_7_11.wrl
http://members.nbci.com/_XMCM/tune_smithy/dekany/cdekany2_1_3_5_7_9.wrl
The black letters are for the inward facing vertices of the outer tetrahedra, (as before,
but mentioning for anyone reading this who hasn't seen the earlier ones).

I've made all the faces opaque for now.

template
http://members.nbci.com/_XMCM/tune_smithy/dekany/dekany_with_diads_template.txt
batch file
http://members.nbci.com/_XMCM/tune_smithy/dekany/do_srvrml2.bat

2)5 dekany with xx = 0.3 in the batch file - easier to see the tetrahedra,
but can't see the diads for the inner edges of the tetrahedra from the outside
http://members.nbci.com/_XMCM/tune_smithy/dekany/cdekany2_0p25_1_3_5_7_11.wrl
http://members.nbci.com/_XMCM/tune_smithy/dekany/cdekany2_0p25_1_3_5_7_9.wrl

3)5 dekany:
http://members.nbci.com/_XMCM/tune_smithy/dekany/cdekany3_1_3_5_7_11.wrl
http://members.nbci.com/_XMCM/tune_smithy/dekany/cdekany3_1_3_5_7_9.wrl
For these, the red spheres are for the utonal triads such as 3*5*9, 3*5*7, 5*7*9,
and are shifted out from the centre of the relevant face.
I've left them that way so that there is more room for the gray tetrad sphere + the text
for the other note of the utonal tetrad (in this case, 3*7*9)

template
http://members.nbci.com/_XMCM/tune_smithy/dekany/dekany3_diads_opaque_faces_for_triads.txt
batch file
http://members.nbci.com/_XMCM/tune_smithy/dekany/do_srvrml3.bat

3)5 dekany with transparent tetrahedra for the tetrads (but doesn't fit in too well with
the text at present)
http://members.nbci.com/_XMCM/tune_smithy/dekany/cdekany3_tetrahedra_triads_1_3_5_7_9.wrl

Notice, I've tried using a decimal point instead of the * for this one,
e.g. 3.5.7
Does that seem a possibility, - makes the text a bit more compact.

http://members.nbci.com/_XMCM/tune_smithy/dekany/cdekany3_tetrahedra_triads_1_3_5_7_11.wrl
template
http://members.nbci.com/_XMCM/tune_smithy/dekany/dekany3_with_diads_faces_for_triads_tetrahedra_for_tetrads~3.txt
batch file
http://members.nbci.com/_XMCM/tune_smithy/dekany/do_srvrml3_tetra.bat

Audio clips listed at head of the .wrl files as usual.

I've commented out all the Sound and Route nodes at the end.

For the version with them uncommented, remove the c in e.g. cdekany3_1_3_5_7_11.wrl
from the url.

- can modify to make any other dekany by replacing same number everywhere in the batch
file to make the .wrl file from the template.

To change the title that you see, edit the .wrl file and look for the line

string "Dekany"

in the first Billboard node.

N.B. as picture of 4D figure, all the faces, including all the triangles, and all the tetrahedra and octahedra
are external (in the same way that all the squares, lines and points are on the outside of a cube) -
there is no internal structure. If one can imagine that. I wonder how many people really are able to
see 4D shapes in 4D.

I imagine rather few, though some have been reported to be able to visualise
4D shapes and answer questions about them by doing so - don't know if that is the
same thing.

Robert