Re: Integer tetrahedron
- From: "snapdragon31" <snapdragon31@xxxxxxxxx>
- Date: 14 Oct 2005 16:58:43 -0700
Dr Tim wrote:
> Does anyone know a tetrahedron with the following properties:
> 1) The volume is a positive integer;
> 2) The edges are all integers;
> 3) None of the faces is a right-angled triangle.
I did it by trial and error.
Bottom triangle has sides 18,41,41
Triangle sides with bottom edge = 18 is 18, 41, 41
Triangle sides with bottom edge = 41 is 41, 41, 24
Let A, B, C are the vertices touch the ground
Let D be the top vertices
Length of AB = 18
Length of BC = 41
Length of CA = 41
Length of AD = 41
Length of BD = 41
Length of CD = 24
All edges are integers and none of the faces is a right-angle triangle.
Area of ABC
= 40 * 9 = 360
Height of the tetrahedron
= 24 * 32 / 40
= 19.2
Volume of the tetrahedron
= 360 * 19.2
= 6912
.
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