The Rule Scales

Two buildings, one rule. Both are built from a single 6.000 m member repeated without variation, and both stand on the same 10.208 m base. Nothing was re-proportioned between them: the second is what the first becomes when the icosidodecahedron is expanded — its twenty triangles and twelve pentagons pushed out from the centre and the gaps patched with a square per edge. Doubling the vertex count multiplies the usable floor area by 3.09.

16.517 m 24.775 m IKOSI-ONE · ICOSIDODECAHEDRON IKOSI-SQUARED · RHOMBICOSIDODECAHEDRON 19.417 m WIDEST ELEVATION 26.724 m WIDEST ELEVATION
IKOSI-ONE 30 / 60 / 32
IKOSI-SQUARED 60 / 120 / 62
DRAG EITHER FRAME · BOTH TURN TOGETHER. EACH SOLID IS FRAMED TO ITS OWN SIZE HERE — TRUE RELATIVE SCALE IS THE ELEVATION ABOVE.
Side by Side
Ikosi-OneIkosi-Squared
SolidIcosidodecahedronRhombicosidodecahedron
Vertices · nodes3060
Edges · members60120
Faces32  (20△ + 12⬠)62  (20△ + 30◻ + 12⬠)
Edge length6.000 m6.000 m
Base Ø10.208 m10.208 m
Height16.517 m24.775 m
Circumradius9.708 m13.398 m
Widest elevation19.417 m26.724 m
Storeys4  (GF–F3)6  (GF–F5)
Usable area466.7 m²1,441.3 m²
Gross area663.2 m²1,984.1 m²
Framed envelope993.1 m²2,073.1 m²