Fig. 901.03

Fig. 901.03 The Basic Disequilibrium 120 LCD Triangle:
12 vertexes surrounded by 10 converging angles12×10=120
20 vertexes surrounded by 6 converging angles20×6=120
30 vertexes surrounded by 4 converging angles30×4=120

The 360 convergent angles must share the 720° reduction from absolute sphere to chorded sphere: 720/360 = 2° per each corner; 6° per each triangle.

All of the spherical excess 6° has been massaged by the irreducibility of the 90° and 60° corners into the littlest corner. .: 3036.

In reducing 120 spherical triangles described by the 15 great circles to planar faceted polyhedra, the spherical excess 6° would be shared proportionately by the 90°-60°-30° flat relationship = 3:2:1.

The above tells us that freezing 60-degree center of the icosa triangle and sharing the 6-degree spherical excess find A Quanta Module angles exactly congruent with the icosa's 120 interior angles.

Copyright © 1997 Estate of R. Buckminster Fuller