Golden Rhombus
A golden rhombus is a rhombus whose diagonals are in the ratio 
, where 
is the golden
ratio.
The half-angle illustrated above is given by
 |  |  |
(1)
|
 |  | ![1/4[pi-tan^(-1)(4/3)]](/National_Library/20161222123739im_/https://mathworld.wolfram.com/images/equations/GoldenRhombus/Inline8.gif) |
(2)
|
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(3)
|
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(4)
|
This gives the identities
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(5)
|
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(6)
|
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(7)
|
Using the equation for the inradius of a rhombus, the inradius of the golden rhombus is found to be
 |  |  |
(8)
|
 |  |  |
(9)
|
and the area
 |  |  |
(10)
|
 |  |  |
(11)
|
 |  |
The faces of the rhombic hexecontahedron and rhombic triacontahedron are golden rhombi.
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quadrilaterals
