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Topic: A Theorem concerning the Trisectors of a Triangle
Replies: 24   Last Post: Nov 10, 1998 12:19 AM

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Douglas J. Zare

Posts: 228
Registered: 12/6/04
Re: A Theorem concerning the Trisectors of a Triangle
Posted: Sep 17, 1998 4:37 PM
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On Thu, 17 Sep 1998, John Conway wrote:
> On Thu, 17 Sep 1998, Russell Towle wrote:
> >[...]
> > Do we see such behavior in tetrahedra, for instance, with a regular
> > Platonic tetrahedron arising from the trisection or quadrisection of a
> > solid angle?

>[...]
> Your question has suddenly produced an interesting thought - maybe
> the 3D version involves a Schlegel diagram for the orthoplex
> (my preferred name for the cross-polytope) in which the vertex figures
> at the vertices of the outer tetrahedron are versions of the Morley figure?
> I don't think it can work for a Euclidean tetrahedron, because there
> doesn't seem to be a spherical version of Morley; but it could conceivably
> work for an ideal tetrahedron in hyperbolic space.


If one trisects the dihedral angles as you suggest, do the opposite
endpoints of the rays of vertices of Morley triangles ever/always form the
vertices of an ideal regular icosahedron?

Douglas Zare




Date Subject Author
9/12/98
Read A Theorem concerning the Trisectors of a Triangle
Den Roussel
9/12/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/13/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Larry Cusick
10/27/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/13/98
Read Re: A Theorem concerning the Trisectors of a Triangle
steve sigur
9/14/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Richard Guy
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Richard Guy
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Richard Guy
9/16/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Floor van Lamoen
9/16/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Floor van Lamoen
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Floor van Lamoen
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Russell Towle
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Russell Towle
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Douglas J. Zare
9/19/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Russell Towle
9/20/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/20/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/18/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Antreas P. Hatzipolakis
11/10/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Den Roussel

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