Kepler-Poinsot Polyhedron #1: Small Stellated Dodecahedron

S-STELLATE-DODECAHEDRON

It was great to meet Alfredo Medina at AU2012.  What a great feeling to make a friend who shares the same passion and also to know he was doing exactly the same thing as I did.  Talking to Alfredo in the shuttle bus going to the AU party at Hard Rock Hotel, I told him that I had studied all the platonic solid geometries and tried to model them in Revit.  Surprisingly he said he had done something similar on Small Stellated Dodecahedron.

Back from Las Vegas to my Revit workshop, I tried to create my version of Small Stellated Dodecahedron.  Starting at Dodecahedron, I could see the Small Stellated Dodecahedron is a further development of the Dodecahedron by adding a pentagonal pyramid at each pentagon face.  So the strategy was: create a pentagonal pyramid, nest it to the dodecahedron, place one pyramid on each face.

Pentagonal Pyramid

This was done with adaptive component family.  With the ease of creating five points spaced equally on the circumference of a circle (with Normalized Curve Parameter), a parametric pentagon could be made.  Simply extrusion and void sweep along the pentagon path made the pentagonal pyramid.

PENTA-PYRAMID1PENTA-PYRAMID2PENTA-PYRAMID3

With a circle on each edge and at the top vertex, a frame was made.  The solid form and the frame are two type options for the pentagonal pyramid.

PENTA-PYRAMID4

Parameters and Math

PENTA-PYRAMID-PARA

Back to the Dodecahedron, 2 types were made: solid form and frame.DODECAHEDRON-FRAME

Placing the Pentagonal Pyramids

The easiest way to place a pentagonal pyramid is on the midpoint of the line joining the first and the third vervex of a pentagon face.  However the orientation of the midpoint is perpendicular to the face of the pentagon face.

Rotating the Pyramid

The pyramid was nested to a new adaptive component  family and rotated 90 degrees.  It was placed with the center of the pentagon base at a point off set from the origin (adaptive point) of the new family.

PENTA-PYRAMID5PENTA-PYRAMID-PARA2

Making the Small Stellated Dodecahedron

When this new family was loaded to the dodecahedron and placed at the midpoint of the line joining two vertice of a pentagon face, the pyramid base would sit on the pentagon face, center to center.

S-STELLATE-DODECAHEDRON2

With a parameter “Pyramid Face Slope” which associates with a parameter in the nested pyramid, the Small Stellated Dodecahedron can have variable height and sharpness of the projecting pyramids.  Parameters are preset to make types for Standard (any two adjacent faces are at the same angle), Equal Edge (all edges are equal), Mass and  Frame.

S-STELLATE-DODECAHEDRON-PARA

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2 responses to “Kepler-Poinsot Polyhedron #1: Small Stellated Dodecahedron

  1. Hi, Kelvin! Yes, that’s one of the great things about AU, that we get to find people who share the same interests, such as figuring out how to model a dodecahedron. It was a pleasure to meet you at AU !

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