### Dodecahedron construction starting from a simple hexagon (cube)

Construction : Start from an hexagon.

Pentagon’s circle is constructed from line draw between point J and I (green line) , intersecting the hexagon’s circle C at point K (center is I ) - plane 2D pentagon construction is detailed later below

- circumference C / circumference P gives ratio 1.86834
- segment’s length CG / LM gives ratio 1.58930
- segment CG/ segment LK gives 0.98224

**Correlations Notes**:

From “ildenir”’s 3d models files, on github , dodécahédron’s 20 vertices coordinates (x,y,z) :

1.21412,0,**1.5893**1,

0.375185,1.1547,**1.5893**1,

-**0.98224**7,0.713644,**1.5893**1,

-**0.98224**7,-0.713644,**1.5893**1,

0.375185,-1.1547,**1.5893**1,

1.96449,0,0.375185,

0.607062,**1.86834**,0.375185,

-**1.5893**1,1.1547,0.375185,

-**1.5893**1,-1.1547,0.375185,

0.607062,-**1.86834**,0.375185,

** 1.5893**1,1.1547,-0.375185,

-0.607062,**1.86834**,-0.375185,

-1.96449,0,-0.375185,

-0.607062,-**1.86834**,-0.375185,

** 1.5893**1,-1.1547,-0.375185,

** 0.98224**7,0.713644,-**1.5893**1,

-0.375185,1.1547,-**1.5893**1,

-1.21412,0,-1.58931,

-0.375185,-1.1547,-**1.5893**1,

** 0.98224**7,-0.713644,-**1.5893**1

dodecahedron from simple hexagon 2D ortho :

- STEP1 : drawing the simple hexagon figure

- STEP2 : using the PHI / Pentagon found point to have some coordinates of the dodecahedron’s figure we want to construct:

create line K-JJ.

JJ is The Point

Draw circle E-JJ : EL is the distance for dodecahedron draw

- STEP3 : using EL all around the circle:

We now have L + M,N,O,P,Q = 6 points more

- STEP4 :

segments are created from L,M,N,O,P,Q to the hexagon’s original points on the circle

- STEP5:

Draw parallels l1,m1,n1. it intersects the hexagon’s axes at S,R,T points

- STEP6-7-8-9:

from R,S,T, construct the dodecahedron’s base pentagon’s edges and the rest of segments :

**Simplest pentagon construction, starting from an hexagon figure :**

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**dodecahedron view from Z, starting from the previous figure :**