A Subset of Phi Space
A Subset of Phi Space
Phi space is the set . The Zome construction system is based on phi space.
{a+bϕ,c+dϕ,e+fϕ},ϕ=,a,b,c∈
1+
5
2
This Demonstration looks at the subset of phi space , that is, where each of and , and , and and have the same parity. Then each element of can be expressed as an integral linear combination of the six half-diagonals of the icosahedron.
X={a+bϕ,c+dϕ,e+fϕ},ϕ=,a,b,c∈,(a+f)2,(b+c)2,(d+e)2∈
1+
5
2
a
f
b
c
d
e
X
The points shown have coefficients , , … at most 3 in absolute value. The convex hull of is a triacontahedron.
a
b
X