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The tale of Platonic Solids

Updated on January 3, 2018
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I have been teaching mathematics in an Australian High School since 1982, and I am a contributing author to many mathematics text books.

platonic

A teacher's portfolio is replete with lesson plans which promise nirvana and deliver purgatory. Semester examinations were over, reports were written and holidays were teasingly around the corner. There was a disquieting sense of calmness permeating throughout the school.

This was ominous. It reminded me of the calm preceding the Spring Offensive of '05, when misguided students rendered inoperative the school's public address system. For several days the Principal acted as errand boy, delivering dispatches and shepherding students into class rooms by an assortment of dramatic gesticulations using an old bell resurrected from a long forgotten store room. The miscreants made good their escape but their legacy remained- the reverberations and the discordant peal of the bell left a lasting impression on everyone.

"Sir," Lino proposed at the beginning of one lesson, "Can we do something fun for a change?"

His request was echoed by others with cries of "Yeah, please sir! You're the greatest."

Intoxicated by their platitudes and suffering from mental aberration, I relented.

"All right, we'll construct a geodesic dome to represent a Platonic solid," I suggested.

"Will that be fun?" Steve asked, even though he did not understand what I had said.

"What are Platonic solids?" Helda enquired, displaying her usual ambition to learn.

"The five Platonic solids are three dimensional shapes that were admired by the ancient Greeks for their beauty." I grabbed some shapes from the display cabinet and held them up. "We have a cube, a tetrahedron, a hexahedron, an octahedron, an icosahedron and a dodecahedron," I said. "Plato associated four of these shapes with physical qualities; earth with the cube, air with the octahedron, water with the icosahedron and fire with the tetrahedron."

The class seemed unimpressed.

"We have an ample supply of wooden rods and plastic connectors to create a giant replica of one of the solids," I informed them. Now there were nods of approval and I was inundated with questions. How big? Where do we build it? Which shape? When?

The following day was overcast and windy; tree branches swayed rhythmically and the school flag snapped at each attempt to break free from its pole. I led the class to a patch of grass adjacent to the gymnasium. Each group collected their ration of building materials and retired to their allocated construction zone to begin the project. I meandered from group to group, witnessing animated conversations and rivalry as each crew raced to be first. Occasionally I called out instructions, but they were drowned by the wind.

To herald the completion of the last lattice framework, a prolonged session of cheering ensued, with students from a nearby class room whistling as accompaniment.

"We haven't finished," I reminded them, "That was the easy part." I was trying to make myself heard above the roar of the wind.

"Now we have to put all the sections together. Remember, team work is required. Let's go."

However, what worked well at the intragroup level did not necessarily portend global success. There was argument concerning which group should be first, ineffectual cries for ladders and colourful instances of quarrelling and haranguing when disagreements arose. "My Tower Of Babel," I mused.

Eventually the monolith took shape. It was at this stage that I began to worry. The icosahedron was larger than I envisaged I estimated about five metres- and its architects remained blissfully unaware of its perilous proximity to the gym's windows.

"Crikey!" the Principal remarked to me as he observed our efforts during his reconnoitre of the yard. "Very impressive, Ekmar, but is it safe?"

"It's as stable as the proverbial Rock Of Gibraltar, Dan," I lied.

Dan was sceptical. "It's swaying all over the place and isn't it a bit too close to the gym?" he queried.

"Well- ," I began as I speculated on the possible fate of any poor soul that might encroach upon the orb's perimeter.

"Jimmy!" Dan called out authoritatively, not waiting for me to finish. Jimmy walked towards us obediently.

"Yes, sir," he said.

"What is that?"

"We made a big colonic solid," he uttered proudly, "Just like sir told us to."

I winced. Dan was nonplussed. As a rule, administrators are not disciples of malapropisms, particularly when scatological connotations are involved.

Dan was about to resume his tour of duty when an unexpected wind shear initiated a sequence of developments that are indelibly printed in our minds. The tensile strength of the rods and the traction on the plastic connectors are no match for the forces of nature. The icosahedron swayed alarmingly, gaining momentum with each precarious oscillation. Succumbing to the inevitable, plastic connectors made popping noises as they parted company with the rods, compelling my class to scurry from the epicentre like ants fleeing their flooded home.

Cries of despair blended with squeals of laughter. And then several errant rods refuted the immutable laws of motion espoused by Newton by puncturing the huge gymnasium windows, transforming thousands of dollars worth of glass into confetti-sized shards resembling hailstones.

Oh, the humanity!

Blessed are the merciful, for they too shall be blessed. In time, armistice was declared and the Principal allowed the curtain of forgiveness to descend upon my teaching career.

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