Never Meet A Polygon Half-Way

The Fremantle Visitor Center email confirmed my booking for the Tuesday Afternoon, 10:30 AM to 12:30 PM, Fremantle History Walking Tour. It gave the starting point as the top of Roundhouse hill near the ship artwork; just to the left of the Roundhouse as you come up the Roundhouse stairs. I’ve always thought that planning to be on time for the start of an event is a bad idea, so I make every effort to arrive fifteen minutes before the announced start time. Google maps suggested it was a 7-minute walk down High Street to the top of Roundhouse Hill, so I left the hotel an hour before the tour start time. High Street was slowly starting to wake; shop keepers were hosing and sweeping the footpath in front of their shops, and small collections of people were starting their day with a flat white and the morning newspaper, at just placed outdoor tables.

image source:jmcadam

There was nothing to hinder my walk down High Street, and I was at the top of Roundhouse hill and near the ship artwork inside of 10 minutes. I was alone. I stood absorbing the panoramic view of the Indian Ocean, Bathers Beach, Fishing Boat Harbour, and the sweeping views over Fremantle and the historic High Street I’d just strolled down. As the sun climbed higher into the morning sky, the waters began to transform into a shimmering azure mirror. Rottnest Island ferries started skating across the blue waters, and one or two container ships began to slowly head toward the container terminal.

I wondered how I’d recognise Big Al, the tour operator and guide for Fremantle History Walking Tours. It wasn’t all that difficult; he was wearing a blue tee-shirt with Fremantle History Walking Tour, in Old English font on the front. Al shared he was a local lad, born and raised in Freo and that he was eager to share his knowledge about his beloved Freo. I thought we had Big Al to ourselves, but when it came time to start the tour, another tourist turned up; obviously someone who always plans to be on time for the start of an event.

image source:jmcadam

Al spoke proudly and passionately about the history of his treasured Fremantle. He drew our attention to the Roundhouse, explaining it was built just after the Swan River Colony was established to hold anyone convicted of a crime in the new settlement. It was Western Australia’s original goal, and is the oldest, still standing, public building in the state. Al highlighted the Roundhouse’s twelve-sides, describing how the cells were arranged around a central courtyard so a warder, at the centre of the building, could see into any open cell. Al had encouraged us to ask questions, so I was tempted to ask

if it has twelve sides why didn’t the early colonists call it a Dodecagon, instead of a Roundhouse?

Big Al began to recite the sad and dark story of the hanging of a young 15-year-old Parkhurst Reformatory boy in front of the Roundhouse. He described John Gavin as a tiny boy, so tiny he had weights attached to him so that his execution was more humane. Al’s recounting of the gruesome crime became white noise because all I was thinking about was polyhedra.


My attention shifted from three- dimensional dodecahedrons when Al pointed to the Roundhouse Stairs and pronounced in a loud voice

and they carried poor Gavin down those stairs to a makeshift gallows not ten yards away, (Big Al lowered his voice at least four octaves to deliver the poignant epilogue) and the prison bell was heard to toll as the melancholy procession set out from Gavin’s cell to the scaffold.

I closed my eyes hoping to clear my mind of the image of the tiny 15-year-old John Gavin hanging in chains from the makeshift gallows. I thought of asking Big Al if the silhouette of the gallows and chains resembled a wireframe pentagram, but he had moved on. He was delivering a passionate narrative about Fremantle’s charming, heritage sandstone buildings.


On the short walk to the WA Shipwrecks Museum, Al delivered his rhetorical précis on the European exploration and settlement of Western Australia. As he talked of Dirk Hartog, Willem Janszoon, and other Dutch, French and English navigators, and Edmund Lockyer and William Dampier, I was transported back and sitting in Mr. McDevitt social studies class at Williamstown Tech. Mr. McDevitt was a chosen one, a gifted master of the blackboard. He created colourful chalkboard panoramas of the exploration of Australia; Blaxland, Lawson and Wentworth crossing the Blue Mountains, Burke and Wills’ fateful crossing of Australia, and the voyages of Bass and Flinders. Sometimes Mr. McDevitt would create his blackboards before class, and as we lined up outside the classroom our eyes were drawn to the blackboard masterpieces. The eyes of every boy were fixated on the sweeping chalk tableau masterpieces as we marched single file into the room.

But not all Williamstown Tech teachers had the same blackboard chalk skills as Mr. McDevitt; compared to Mr. McDevitt they were blackboard amateurs. Mr. Stonehouse taught first, second, and third form Arithmetic. He kept his chalk in its original cardboard box, on the table at the front of the room. He’d reach into the chalk box for a stick of white chalk, raise it to his mouth and lick it, step up to the board, and with his back to the class, produce the working out for the problems he’d just set the class. Within seconds, the front of the classroom was a cloud of white chalk dust.

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Mr. Fraser’s blackboards were formal, organised, and laid out with scientific precision. He taught general science to 4AB, and chemistry and physics to 5AB. In the fourth form, we watched Mr. Fraser perform experiments on the front of the room teacher’s science bench. And the assembled equipment appeared in coloured chalk on the front boards, along with a detailed description of the method, observations and measurements, calculations, and conclusions. His blackboards were chalk journals. When there wasn’t an experiment, Mr. Fraser, with his back to the class, filled the three boards with precise, chalk written, scientific theories, postulates, and laws. The boards were a mirror copy of a chapter in a science textbook.

Mr. Baldwin taught fourth and fifth form Mathematics. Fifth form Mathematics was divided into Algebra, Trigonometry, and Geometry. Mr. Baldwin’s blackboards were of a similar standard to Mr. Frasers. They were filled with rows of neat algebraic equations, right-angle triangles with only an angle and the length of a side labeled, and parallel lines cut by transversals. But that’s not how I remember Mr. Baldwin. I don’t know how, or exactly when, he knew that the post-pubescent teenage boys of 5AB were ready to see the three dimensional cardboard models.


One day, halfway through a geometry class, he disappeared through the door in the front corner of the room, and into his office. He reappeared within minutes carrying a mysterious shape and stepped onto the raised platform at the front of the room. Mr. Baldwin slowly twisted and turned the strange cardboard model, as he raised it above his head. I remember staring with wide-open eyes as he moved and turned the model because every face was an exact copy of the other. He challenged us to count the number of faces and polygons in the model and commanded

and when you have the answer boys hands up

Mr. Baldwin caused time to stop for several minutes by waiting for a show of hands. There were three standard hand-raising techniques we used. Each one was used to signal that you had an answer to a question, or as a distraction decoy if you hadn’t a clue. A good hands up strategy, to cause the teacher to wonder if you had an answer or not, was to never use the same hand-raising technique twice in the same class period.

Sputnik blast off: the arm is pushed at top speed until it’s at a straight vertical line from the shoulder
Pumping up the flat bike tyre: the arm is slowly raised from the shoulder and the action is repeated so the arm is continually raised and lowered
Stopping the car hand signal: the arm is slowly pushed out from the shoulder until is at 90 degrees to the body and then it is bent at a 45 degree angle to elbow bend it at the elbow. The index finger is usually raised when the arm reaches it’s resting position


John Colville and Robert Ballard always did the Sputnik blast off hand-raising technique. Which was to be expected because they were the brains of 5AB and had no need to use deception or bluff. Mr. Baldwin waited for fifteen hands in the air and then announced

class, hands down; (he waited, enjoying the silence) boys this is Mr. Dodecahedron

Mr. Baldwin seemed to sense an excitement and wonderment that not one of the 5AB boys experienced. He went into his office and was back in a flash standing in front of the room, holding another model above his head. He announced to us stupefied boys: I hold the trisoctahedron. In the following weeks, Mr. Baldwin showed us cardboard models of hexoctahedrons, dodecagonals, and other polyhedra. Sometimes during a geometry class, he’d call a lucky boy to the front of the room and allow them to hold the polyhedra. I think he was hoping one of us would raise our hand and ask

sir can I hold the polyhedra, do you have any irregular pentahedrons sir, how long did it take you to make the truncated icosahedron sir

Mr. Baldwin didn’t seem to understand that post-pubescent boys didn’t have a curiosity about polyhedra; that we had other things to think about instead of the geometry of three-dimensional polyhedrons.

image source:jmcadam

Big Al finished his tour at the corner of Marine Terrace and Collie Street. As we sat and socialised on the street benches by Esplanade Park, I asked him if he had considered offering a polyhedra walking tour of Fremantle. In a city whose heritage buildings capture the timeless balance between man, land, and the sea, there had to be remarkable architectural examples of icosahedrons, cubicuboctahedrons, and rhombic triacontahedrons. Al said he would think about it.


WA Shipwrecks Museum

Fremantle Roundhouse

How To Make A Dodecahedron