Read here about tensegrity structures composed of 540 struts, part of a series of pages organized by strut count.

92 Prism Tensegrity


Photographs dated to April 1979 show R. Buckminster Fuller holding a tensegrity sphere composed of 92 Prisms. Its structure, as analyzed by Taffgoch and Adrian Rossiter is summarized below.

RBF with 92 prism tensegrity 19790418 B.jpg
RBF with 92 prism tensegrity, April 1979

RBF with 92 prism tensegrity 19790418.jpg
RBF with 92 prism tensegrity, April 1979

Tensegrity Prism 960 struts by Taffgoch.png
Tensegrity Prism 960 struts by Taffgoch

Tensegrity Prism Animated Overlay by Taffgoch.gif
Tensegrity Prism Animated Overlay by Taffgoch

Tensegrity Prism inner tendons icosa by Taffgoch.png
Tensegrity Prism inner tendons icosahedron shown by TaffGoch

Tensegrity Prism one highlighted by Taffgoch.png
Tensegrity Prism one highlighted by Taffgoch

Tensegrity Prism outer and inner tendons icosa by Taffgoch.png
Tensegrity Prism outer and inner tendons by TaffGoch

Tensegrity Prism outer tendons icosa by Taffgoch.png
Tensegrity Prism outer tendons icosa by TaffGoch


The sphere is a tensegrity sphere, composed of many adjacent prism tensegrties
See "prism" tensegrities: http://tensegritywiki.com/Prism

Mexican method 6V sphere, composed of 92 prisms. 540 struts total
12 pentagonal prisms. = 60 struts.
80 hexagonal prisms = 480 struts

Assuming uniform struts (all the same length), the pentagonal prisms will be 20% higher if they had the same approximate edge length as the hexagons. This longer edge should be visible in the photograph, and may result in a slight twist.

The tendon nets can be comprehended by outer, inner and interstitial
Outer purple
Inner blue
Interstitial orange

The tendon nets could be continuous. "An undirected graph has an Eulerian cycle if and only if every vertex
has even degree, and all of its vertices with nonzero degree belong to
a single connected component."


Each prism has a winding direction.

To physically construct this tensegrity: Since each prism is rigid, each can be assembled separately, then connected to adjacent prisms, by the corners (not the edges.)

To construct this tensegrity in Rossiter's Antirpsim dome_layer program:

// tens_strut_string.inc

#include "woods.inc"
#include "metals.inc"

#macro disp_edge(edge, col)
#if(!v_equal(verts[edges[edge][0]], verts[edges[edge][1]]) )
#if (col.x=0)
cylinder{verts[edges[edge][0]] verts[edges[edge][1]] edge_sz
texture{ T_Wood3 }
}
#end
#if (col.x=1)
cylinder{verts[edges[edge][0]] verts[edges[edge][1]] edge_sz/3
texture{pigment{colour <0.8, 0.8, 0.6>}}
}
#end
#end
#end

I have attached images showing the result of applying it to a
spherical 3F icosahedron dual (the commands will be valid
for the next snapshot of Antiprism, 23.99+07 or greater). One
is the basic model viewed in Antiview

dome_layer -t prism geo_3_d | antiview -v 0.015

The other is a the model processed by off2pov, with a custom include
file, and rendered in POV-Ray

off_trans -y D5 geo_3_d | dome_layer -i -t prism | off_color -e M -m map_0:1:1:1 | off2pov -v 0.015 -i tens_strut_string.inc > pri_tens_geo_3_d.pov

[off_trans -y lines up the model on a 5-fold axis. dome_layer -i uses
index numbers for colouring. The off_color command makes the strut
colour 0 and the strings colour 1. off2pov converts it to POV-Ray
format, and the custom include file tens_strut_string.inc (included
below) draws the elements to make the model look like a tensegrity.]

On my system, I rendered this with

povray declare=AspectRatio=1 +a +p +H2000 +W2000 pri_tens_geo_3_d.pov

A similar 4V is proposed by TaffGoch. This Mexican method 4V sphere, composed of 42 prisms. 240 struts total
12 pentagonal prisms. = 60 struts.
30 hexagonal prisms = 480 struts



WORK IN PROGRESS

Links and References




Portal to Polyhedra
A series on polyhedra and associated tensegrities
  1. Platonic: Cube, Dodecahedron, Icosahedron, Octahedron, Tetrahedron
  2. Archimedan: Cuboctahedron, Jitterbug, Rhombic Dodecahedron, Stella Octangula, Tricontahedron
  3. Form: Prism, Torus
  4. Concepts: Naming
Access by no. of struts: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 21, 30, 60, 90, 270, 540; Procedures: 3, 30