The following Cartesian coordinates define the vertices of an icosahedron with edge-length 2, centered at the origin:
(0, ±1, ±φ)
(±1, ±φ, 0)
(±φ, 0, ±1)
where φ = (1+√5)/2 is the golden ratio (also written τ). Note that these vertices form five sets of three concentric, mutually orthogonal golden rectangles, whose edges form Borromean rings.
If the original icosahedron has edge length 1, its dual dodecahedron has edge length , one divided by the golden ratio.
Gold nanoparticle - monoatomic gold - alchemy symbolic transmutation
Luca Pacioli - gyroscope -borromean rings - hourglass
Luca Pacioli - icosahedron - Sem priest - Leopard skin
Earth grid - Phi - Icosahedron
Dali Tiger - The beast
William Blake Tyger poem
TIGER, tiger, burning bright
In the forests of the night,
What immortal hand or eye
Could frame thy fearful symmetry?
In what distant deeps or skies
Burnt the fire of thine eyes?
On what wings dare he aspire?
What the hand dare seize the fire?
And what shoulder and what art
Could twist the sinews of thy heart?
And when thy heart began to beat,
What dread hand and what dread feet?
What the hammer? what the chain?
In what furnace was thy brain?
What the anvil? What dread grasp
Dare its deadly terrors clasp?
When the stars threw down their spears,
And water'd heaven with their tears,
Did He smile His work to see?
Did He who made the lamb make thee?
Tiger, tiger, burning bright
In the forests of the night,
What immortal hand or eye
Dare frame thy fearful symmetry?
The Lamb
William Blake
Little Lamb, who made thee
Does thou know who made thee
Gave thee life & bid thee feed.
By the stream & o'er the mead;
Gave thee clothing of delight,
Softest clothing woolly bright;
Gave thee such a tender voice.
Making all the vales rejoice:
Little Lamb who made thee
Does thou know who made thee
Little Lamb I'll tell thee,
Little Lamb I'll tell thee;
He is called by thy name,
For he calls himself a Lamb:
He is meek & he is mild,
He became a little child
I a child & thou a lamb,
We are called by His name,
Little Lamb God bless thee,
Little Lamb God bless thee.