perplexus.info :: Geometry : Dodecahedron

Dodecahedron (Posted on 2005-03-24)

A regular dodecahedron has 12 pentagonal sides and 20 vertices. Assuming the bottom face is lying on the X-Y plane, above the X-axis, with one edge along (0,0,0)-(0,1,0), what are the coordinates of the remaining 18 vertices?

See The Solution Submitted by Erik O.

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Comment 2 of 2 |

The required 18 vertices are:

x y z

1.53884176858763 0.50000000000000 0

1.37638192047117 1.00000000000000 2.22703272882322

0.95105651629515 1.30901699437495 0

0.42532540417602 1.30901699437495 2.22703272882322

0.00000000000000 1.00000000000000 0

-.16245984811645 0.50000000000000 2.22703272882322

0.00000000000000 0.00000000000000 0

0.42532540417602 -.30901699437495 2.22703272882322

0.95105651629515 -.30901699437495 0

1.37638192047117 -.00000000000000 2.22703272882322

2.06457288070676 0.50000000000000 .850650808352039

1.80170732464720 1.30901699437495 1.37638192047118

1.11351636441161 1.80901699437495 .850650808352039

0.26286555605957 1.80901699437495 1.37638192047118

-.42532540417602 1.30901699437495 .850650808352039

-.68819096023559 0.50000000000000 1.37638192047118

-.42532540417602 -.30901699437495 .850650808352039

0.26286555605957 -.80901699437495 1.37638192047118

1.11351636441161 -.80901699437495 .850650808352039

1.80170732464720 -.30901699437495 1.37638192047118

Edited on May 14, 2024, 12:37 am

Posted by K Sengupta on 2024-05-14 00:36:38

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