WOLFRAM|DEMONSTRATIONS PROJECT

Tree of Spikeys

​
number of helices
1
2
3
4
5
number of branches
1
2
3
4
5
6
add Spikey
0
1
2
3
4
5
6
separate branches
rotate
expand
shrink
The tree structure shown has a stem of rhombic hexecontahedra (RHs). Additional RH branches are attached to each RH in the stem. The golden ratio
ϕ
appears in the structure: an RH consists of golden rhombuses; the sizes and the distances of the subsequent RHs in the tower are related to one another in the proportion of the golden ratio. The tilting angle
2arctan(1/ϕ)
is also related to the golden ratio. The total height of the infinite series of RHs in the stem is also related to the golden ratio.