Mathematical Models
![](../model_photos/fac_sci_display/model_display01.jpg)
A few years ago, I began making mathematical models as a hobby. I have since made complete sets of Platonic solids and Archimedean solids as well as numerous other polyhedra, including a number featured in the designs of Leonardo da Vinci. Some of my models are now featured in a display on the ground floor of Machray Hall.
Brookside Monument
In 2003, the University of Manitoba sponsored the construction of a large memorial for the Brookside Cemetery in Winnipeg, Manitoba in dedication to those who had donated their bodies to science. Based on an idea by Wayne Larson, I designed a monument in the form of a heptahedron.
Gallery of Models
- Platonic solids
- Archimedean solids
- Open-faced da Vinci models
- Truncation
- Other Polyhedra
- Space-filling solids
- Puzzles
- Dissections
- Paper models
- Miscellaneous pieces
Platonic solids
Back to topCube
![Cube](../model_photos/platonic/cube.jpg)
Six square faces: two each of ebony, cocobolo, and bubinga.
Dodecahedron
![Dodecahedron](../model_photos/platonic/dodecahedron.jpg)
Twelve pentagonal faces made of oak, black walnut, chokte kok, narra, mahogany, ebony, zircote, osage orange, birdseye maple, bubinga, purple heart, and cherry.
Icosahedron
![Dodecahedron](../model_photos/platonic/icosahedron.jpg)
Four faces each of kingwood, birdseye maple, bocote, cocobolo, and santos rosewood. All five woods meet at each vertex.
Octahedron
![Octahedron](../model_photos/platonic/octahedron.jpg)
Four faces each of chestnut and bocote.
Tetrahedron
![Tetrahedron](../model_photos/platonic/tetrahedron.jpg)
Four faces: one each of tulipwood, purple heart, padauk, and ebony.
![Tetrahedron](../model_photos/platonic/maple_tetrahedron.jpg)
Hollow with 5 inch edge lengths. Made from maple.
Archimedean Solids
Back to topCuboctahedron
![Cuboctahedron](../model_photos/archimedean/cuboctahedron.jpg)
Fourteen faces: eight triangles made from chestnut and 6 squares made from ebony.
Great rhombicosadodecahedron
![Great rhombicosadodecahedron](../model_photos/archimedean/great_rhombicosadodecahedron.jpg)
Sixty-two faces: 12 decagons made from maple veneer on plywood, 30 squares made from walnut, and 20 hexagons made from cherry.
Great rhombicuboctahedron
![Great rhombicuboctahedron](../model_photos/archimedean/great_rhombicuboctahedron.jpg)
Twenty-six faces: 12 squares made from zircote, 8 hexagons from osage orange (bowwood), and 6 octagons from bubinga.
Icosidodecahedron
![Icosidodecahedron](../model_photos/archimedean/icosidodecahedron.jpg)
Thirty-two faces: 20 triangles made from mahogany and 12 pentagons made from maple.
Lesser rhombicosadodecahedron
![Lesser rhombicosadodecahedron](../model_photos/archimedean/lesser_rhombicosadodecahedron.jpg)
Sixty-two faces: 12 pentagons made from chokte kok, 20 triangles from kingwood, and 30 squares from cherry.
Lesser rhombicuboctahedron
![Lesser rhombicuboctahedron](../model_photos/archimedean/lesser_rhombicuboctahedron.jpg)
Twenty-six faces: 18 squares made from teak and 8 triangles from tulipwood.
Snub cube
![Snub cube](../model_photos/archimedean/snub_cube.jpg)
Thirty-eight faces: 32 triangles made from purple heart and maple and 6 squares from hickory.
Snub dodecahedron
![Snub dodecahedron](../model_photos/archimedean/snub_dodecahedron.jpg)
Ninety-two faces: 80 triangles and 12 pentagons made from walnut.
Truncated cube
![Truncated cube](../model_photos/archimedean/truncated_cube.jpg)
Fourteen faces: 6 octagons made from bubinga and 8 triangles from maples.
Truncated dodecahedron
![Truncated dodecahedron](../model_photos/archimedean/truncated_dodecahedron.jpg)
Thirty-two faces: 20 triangles made from walnut and 12 decagons from mahogany. Made entirely from recovered wood: the mahogany planks were once bookshelves.
Truncated icosahedron
![Truncated icosahedron](../model_photos/archimedean/truncated_icosahedron.jpg)
Thirty-two faces: 12 pentagons made from walnut and 20 hexagons from maples.
Truncated octahedron
![Truncated octahedron](../model_photos/archimedean/truncated_octahedron.jpg)
Fourteen faces: 6 squares and 8 hexagons, all made from bloodwood.
Truncated tetrahedron
![Truncated tetrahedron](../model_photos/archimedean/truncated_tetrahedron.jpg)
Eight faces: 4 hexagons made from purple heart and 4 triangles from lemon heart (pau amarello).
Open-faced da Vinci models
Back to topSet of 5 open-faced Platonic solids
![Five open-faced Platonic solids](../model_photos/open_faced_da_vinci/platonic_05.jpg)
Each of these models is made with 5-inch edge lengths and all models are made from mahongany with 12, 12, 24, 60, and 60 pieces respectively.
Open-faced rhombicuboctahedron
![Rhombicuboctahedron](../model_photos/open_faced_da_vinci/rhombicuboctahedron_01.jpg)
Made from 96 pieces of pine, entirely recovered wood.
Open-faced Campanus sphere
![Campanus sphere](../model_photos/open_faced_da_vinci/campanus_12.jpg)
Made from 264 pieces of obeche (also known as wawa).
Open-faced truncated icosahedron
![Truncated icosahedron](../model_photos/open_faced_da_vinci/truncated_icosahedron.jpg)
Made from 180 pieces of wenge. Each face has the pieces of the polygon dowelled together at the joints and all face-face joints (except two) are biscuit-joined. To test the strength of this model, I once did a handstand on it.
The construction of this model is documented here.
Open-faced icosidodecahedron
![Icosahedron](../model_photos/open_faced_da_vinci/open_faced_icosidodecahedron_01.jpg)
Made from 120 pieces of Goncalo Alves (also known as tigerwood). This model is on display in the Department of Mathematics office.
![Icosahedron](../model_photos/open_faced_da_vinci/toussaint_icosidodecahedron.jpg)
My first open-faced icosidodecahedron, also made from tigerwood. This model was presented to Godfried Toussaint as a 60th birthday gift.
Open-faced stellated octahedron
![Stellated octahedron](../model_photos/open_faced_da_vinci/stellated_octahedron.jpg)
Made of cherry, 5 inch edge lengths. Based on the following drawing by Da Vinci.
![Da Vinci stellated octahedron](../model_photos/open_faced_da_vinci/page101.jpg)
Truncation
Back to topTruncating the cube
![Truncating the cube](../model_photos/truncation/truncating_the_cube.jpg)
Five pieces: all solid and cut from one piece of cherry.
Truncating the cuboctahedron
![Truncating the cuboctahedron](../model_photos/truncation/truncating_cuboctahedron.jpg)
A cuboctahedron truncated to give a great rhombicuboctahedron. Both pieces are made from solid mahogany and are roughly 2 inches in diameter.
Truncating the tetrahedron
![Truncating the tetrahedron](../model_photos/truncation/truncating_tetrahedron.jpg)
Two pieces made from solid cherry.
Truncated dodecahedron
![Truncated dodecahedron](../model_photos/truncation/truncated_dodecahedron_crab_apple.jpg)
Approximately 2 inches in diameter, wood from a crabapple tree.
Other polyhedra
Back to topRhombic Triacontahedron
![Rhombic Triacontahedron](../model_photos/other_polyhedra/rhombic_triacontahedron02.jpg)
Thirty faces made from tigerwood, approximately 3/4 inches thick.
Icosahedron and dodecahedron
![Icosahedron and dodecahedron](../model_photos/other_polyhedra/dodecahedron_icosahedron.jpg)
The icosahedron is made of solid maple and the dodecahedron from solid mahogany. Both are approximately 2.5 inches high.
Truncated cube, cuboctahedron, rhombicuboctahedron, and octahedron
![Four solids](../model_photos/other_polyhedra/four_solids.jpg)
Dissected cube
![Dissected cube](../model_photos/other_polyhedra/half_cubes.jpg)
Two identical pieces made from oak.
Tetrahedron inscribed in a cube
![Tetrahedron inscribed in a cube](../model_photos/other_polyhedra/tetrahedron_inside_cube.jpg)
Made from coffee sticks.
Icosahedron
![Icosahedron](../model_photos/other_polyhedra/3_rectangles_icosahedron.jpg)
Vertices are corners of three golden rectangles that appear to go through each other (an impossible structure).
Pentagonal antiprism
![Pentagonal antiprism](../model_photos/other_polyhedra/pentagonal_antiprism.jpg)
Solid, possibly made from silky oak.
Golden crystal
![Golden crystal](../model_photos/other_polyhedra/golden_crystal.jpg)
My own invention: each face is either a golden rectangle or a golden triangle, of which there are two types. Made from solid MDF, painted gold and varathaned.
Pentagonal trapezohedron
![Pentagonal trapezohedron](../model_photos/other_polyhedra/pentagonal_trapezohedron.jpg)
Made from 10 pieces of one inch thick obeche. Face angles are 108° and 36° and all dihedral angles are the same. This is sometimes mistakenly called a pentagonal deltohedron. This is the dual polyhedron for the pentagonal antiprism.
Space-filling solids
Back to topRhombhex dodecahedra
![Rhombhex dodecahedra](../model_photos/space_filling/rhombhex_dodecahedron_one.jpg)
Seventeen pieces made from cherry and walnut in a plexiglass case.
![Rhombhex dodecahedron](../model_photos/space_filling/rhombhex_dodecahedron_two.jpg)
Made from solid oak.
Cuboctahedra
![Cuboctahedra](../model_photos/space_filling/truncated_octahedra.jpg)
Seventeen pieces: made from an unknown rare wood.
Rhombic dodecahedron
![Rhombic dodecahedron](../model_photos/space_filling/rhombic_dodecahedron_one.jpg)
Made from walnut.
![Rhombic dodecahedron](../model_photos/space_filling/rhombic_dodecahedron_two.jpg)
![Rhombic dodecahedron](../model_photos/space_filling/rhombic_dodecahedron_three.jpg)
Rhombic dodecahedron constructed from an inner cube, perhaps made from aspen, and six cherry pyramids attached with dowels.
Hexagonal prisms
![Hexagonal prisms](../model_photos/space_filling/hexagonal_prisms.jpg)
Around twenty pieces made from solid oak. All edge lengths are 1 inch.
Parallelepipeds
![Parallelepipeds](../model_photos/space_filling/parallelepipeds.jpg)
Six or more pieces: Rhombic parallelepipeds made from spruce with all edge lengths the same. Approximately 2 inches high.
K-dron
![K-dron](../model_photos/space_filling/kdron02.jpg)
![K-drons](../model_photos/space_filling/kdron01.jpg)
Ten pieces made from solid cherry, approximately 2 inches high.
Penrose tiles
![Penrose tiles](../model_photos/space_filling/penrose_tiles.jpg)
Approximately 300 pieces, each made form two golden triangles. This set was donated to the Math Club.
Puzzles
Back to topDovetail
![Dovetail cube](../model_photos/puzzles/dovetail.jpg)
Made from walnut and beech.
Drive ya crazy
![Drive ya crazy](../model_photos/puzzles/drive_ya_crazy_01.jpg)
Made from purpleheart and tulipwood. Awarded as first prize for the High School Math Workshop in January 2004.
![Drive ya crazy](../model_photos/puzzles/drive_ya_crazy_02.jpg)
Case is made from ebony and bloodwood. Hidden door, attached with magnets, and hidden compartment for solutions. Inside are six cubes each with six colours.
Hole in a triangle
![No hole in a triangle](../model_photos/puzzles/hole_triangle_01.jpg)
![Hole in a triangle](../model_photos/puzzles/hole_triangle_02.jpg)
Four movable pieces of maple in a mahogany case.
![Hole in a triangle](../model_photos/puzzles/hole_triangle_04.jpg)
Frame made from maple, base from purpleheart, two pieces from cherry, and two mahogany.
O'Beirne's melting box
![O'Beirne's melting box](../model_photos/puzzles/obeirne_box.jpg)
Four teak and five mahogany blocks. The case is made from maple and walnut.
Pentominoes
![Pentominoes](../model_photos/puzzles/pentominoes.jpg)
Twelve mahogany pieces in a mahogany case.
Sliding box puzzle
![Sliding puzzle box](../model_photos/puzzles/puzzle_box_01.jpg)
![Sliding puzzle box](../model_photos/puzzles/puzzle_box_04.jpg)
Made from zircote and bloodwood.
World's hardest two-piece puzzle
![Two-piece puzzle](../model_photos/puzzles/three_piece_puzzle.jpg)
Three pieces of rosewood and the case is made of walnut. My own design: an extension of the standard two piece dissection of the tetrahedron.
Towers of Hanoi
![Towers of Hanoi](../model_photos/puzzles/towers_of_hanoi.jpg)
Disks made from gaboon ebony and the base is made from vera wood.
Dissections
Back to topSquare-triangle hinged dissection
![Square-triangle dissection](../model_photos/dissections/triangle_square_01.jpg)
![Square-triangle dissection](../model_photos/dissections/triangle_square_02.jpg)
![Square-triangle dissection](../model_photos/dissections/triangle_square_03.jpg)
![Square-triangle dissection](../model_photos/dissections/triangle_square_04.jpg)
![Square-triangle dissection](../model_photos/dissections/triangle_square_05.jpg)
Mahogany and brass hinges.
Pentagon-triangle hinged dissection
![Pentagon-triangle dissection](../model_photos/dissections/triangle_pentagon.jpg)
Mahoany with brass hinges. Approximately 6 inches across.
Hexagon-triangle hinged dissection
![Hexagon-triangle dissection](../model_photos/dissections/triangle_hexagon.jpg)
Made from mahogany, probably African mahogany. Tape hinges.
Copies of the pentagon-triangle and hexagon-triangle dissection were made for Greg Frederickson. They can be seen at his website.
Paper models
Back to topKepler-Poinsot solids
![Small stellated dodecahedron](../model_photos/paper_models/small_stellated_dodecahedron.jpg)
![Great icosahedron](../model_photos/paper_models/great_icosahedron.jpg)
![Great stellated dodecahedron](../model_photos/paper_models/great_stellated_dodecahedron.jpg)
![Great dodecahedron](../model_photos/paper_models/great_dodecahedron.jpg)
Small stellated dodecahedron, great icosahedron, great stellated dodecahedron, and the great dodecahedron
Csaszar polyhedron
![Csaszar polyhedron](../model_photos/paper_models/csaszar.jpg)
Seven vertices, each pair joined by an edge.
Szilassi polyhedron
![Szilassi polyhedron](../model_photos/paper_models/szilassi.jpg)
Seven faces, each pair share an edge.
Rhombic tricontahedron
![Rhombic tricontahedron](../model_photos/paper_models/rhombic_tricontahedron.jpg)
Pentagonal deltohedron
![Pentagonal deltohedron](../model_photos/paper_models/pentagonal_deltohedron.jpg)
14th stellation of the icosahedron
![14th stellation of the icosahedron](../model_photos/paper_models/14_stellation_icosahedron.jpg)
Others
![Four folded polyhedra](../model_photos/paper_models/four_folded_polyhedra.jpg)
Four folded polyhedra. The orange figure is a compound of two cubes.
Miscellaneous pieces
Back to topHexaflexahedron
![Hexaflexahedron](../model_photos/misc/hexaflexahedron_01.jpg)
Six tetrahedra made from solid cherry, connected with brass hinges.
Four triangles interlocking
![Interlocking triangles](../model_photos/misc/four_intersecting_triangular_rings.jpg)
Made from santos rosewood, chakte kok, kingwood, and birdseye maple. Modelled after a carboard version that appeared on the cover of The Mathematical Intelligencer.
![Intelligencer cover](../model_photos/misc/mathematical_intelligencer.jpg)
Trefoil knot
![Trefoil knot](../model_photos/misc/trefoil_knot_one.jpg)
Hand carved from bloodwood.
![Cubic trefoil knots](../model_photos/misc/trefoil_knot_two.jpg)
Enantiomorphic pair of `cubic' trefoil knots, each made from 1 × 1 × 2 blocks.
Möbius band
![Mobius band](../model_photos/misc/mobius_strip.jpg)
Five layers of laminated maples veneer, invisible seams.
Hyperboloid of one sheet
![Hyperboloid](../model_photos/misc/hyperboloid_of_one_sheet.jpg)
Made from oak dowels with top and bottom made from MDF.
Plug filling three holes
![Three-way plug](../model_photos/misc/three_way_plug_01.jpg)
Template made from bloodwood and the plug is made from oak.
Trammel
![Trammel](../model_photos/misc/trammel.jpg)
Cherry base, rosewood arm, mahogany slide and solid brass handle (which moves in an ellipse).
Initial blocks
![Initial block](../model_photos/misc/dsg_block.jpg)
Approximately 2 inches high; perhaps maple.
![D](../model_photos/misc/letter_d.jpg)
![S](../model_photos/misc/letter_s.jpg)
![G](../model_photos/misc/letter_g.jpg)
![Initial block](../model_photos/misc/krj_block.jpg)
Made from solid mahogany.
![K](../model_photos/misc/letter_k.jpg)
![R](../model_photos/misc/letter_r.jpg)
![J](../model_photos/misc/letter_j.jpg)
Mutually orthogonal latin squares
![Mutually orthogonal latin squares](../model_photos/misc/MOLS_finished.jpg)
Twenty triangles each of bubinga, zebrawood, lemonwood (pau feraro), padauk, and grey elm. Frame and inserts made from walnut.
Nailless Nailbanger's Nightmare
![Dome](../model_photos/misc/dome.jpg)
Spruce pieces fitted together without nails or glue. It is a partially finished 'nailless' version of George Hart's Nailbanger's Nightmare. This model was featured in an article by George Hart for his Math Monday column.
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