Basically, you are looking for the area and volume of a tetrahedron.
Tetrahedron area = sq root (3) * edge^2
Tetrahedron area =
<span>
<span>
<span>
27.7128129211
</span>
</span>
</span>
Tetrahedron volume = [sq root (2) / 12] * edge^3
Tetrahedron volume =
<span>
<span>
<span>
0.1178511302
</span>
</span>
</span>
* 64
Tetrahedron volume =
<span>
<span>
<span>
7.5424723327
</span>
</span>
</span>
<span>
<span>
</span></span>
I don't know exactly what you mean by the "lateral area". I'm guessing it is the area of each face?
If that's the case then it equals <span>
<span>
27.7128129211
</span>
/ 4 = </span><span><span><span>6.9282032303
</span>
</span>
</span>
<span>
Source:
http://www.1728.org/platonic.htm
</span>
The 7th term is 24 with a common ratio 4/3)