## Archive for January, 2015

### Icosahedron

2015-01-29

The icosahedron has 12 equilateral triangles as faces. It can be split into 3 parts, a pentagonal anti-prism and two pentagonal pyramids. We will start by looking at a pentagonal pyramid. We have already done most of the work earlier. To find ∠ACB, \begin{align}\cos \angle …Read the Rest

### Dodecahedron

2015-01-28

The dodecahedron is a regular polyhedron made of 12 regular pentagon faces. A D12 die is often used in certain role playing games. Since a dodecahedron has 12 sides, you can print out a calendar, one month per face, and have a conversation piece on …Read the Rest

### Pentagon

2015-01-02

A regular pentagon has the following dimensions: AB=BC=CD=DE=AE=BG=EG=1 AC=AD=BD=BE=CE=Φ BF=EF=Φ/2 = cos 36 = sin 54 = $\frac{1+\sqrt5}{4}$ CG=DG= Φ-1 = 1/Φ = $\frac{\sqrt5-1}{2}$ AF=FG= cos 54 = sin 36 = $\sqrt{\frac{5-\sqrt5}{8}}$ AG= 2cos 54 = 2sin 36= $\sqrt{\frac{5-\sqrt5}{2}}$ CH=DH=BK=CK=1/2 Height AH=EK=\(\frac12\cos 18 = \frac12\sin …Read the Rest

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