Another Chart

From the Synergeo list (# 59600):

XYZ provides a "treatment" whereby all polyhedra will be smaller than their corresponding IVM values, per constant. Here's a chart, which includes [the] 2.8284... cube (XYZ treatment of Syn Cube of 3).

shape	xyz volume in cubic units (cube diagonal is two units)	ivm volume in tetrahedral units (tetrahedron edge is one unit)
A,B	0.0393	0.04166666667
Mite	0.3536	0.125
Tet.	0.9428	1
Cubo.	2.357	2.5
Cube	2.8284	3
Oct.	3.7712	4
Rt.	4.714	5
Rd.	5.6569	6
Rt.	7.071	7.5
Pd.	14.721	15.35
Ico.	17.454	18.512
Cubo.	18.856	20
Cube	22.627	24

Cubo. = cuboctahedron; Rt. = rhombic triacontahedron; Pd. = pentagonal dodecahedron; Rd. = rhombic dodecahedron; Ico. = icosahedron; Oct. = octahedron; Tet. = tetrahedron; Mite = minimum tetrahedron

In collaboration with Alan Michelson

X-ref:

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