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This gallery shows some of the essential mathematical figures that can be constructed with JOVO Click 'N Construct toys, and some of their important properties and relationships. To view the interactive 3D models on this page you will have to have a VRML Viewer installed on your computer. To learn more about this, check out my Help Page. Remember that these are computer generated models that I put here for you to explore, but they are not photographs of the actual models. If you want to see what the models look like when made with the Jovo pieces, make sure you visit my Pictures Page
This gallery will be continually expanding, and submissions and suggestions are always welcome. If you need any help understanding or building one of these models, feel free to e-mail me.
Alex@JovoToys.com
Since the standard JOVO set includes triangles, squares and pentagons, the figures below are shown using just those shapes (using all six colors of JOVO - red, yellow, green, blue, black and white). If a hexagon is needed, you can substitute six triangles. If you need an octagon or decagon, I have the figure "greyed out" to show it cannot be constructed as-is using JOVO. If you wanted to approximate, you can sometimes substitute a square cupola for an octagon, or a pentagonal cupola for a decagon. If you ever need a dodecagon, you can build one from triangles and squares (see prisms and antiprisms below).
| Convex Polyhedra | |||||||||
| Platonic Solids (a.k.a. regular solids - every face is the same, and every vertex is the same) | |||||||||
Tetrahedron![]() |
Cube![]() |
Octahedron![]() |
Dodecahedron![]() |
Icosahedron![]() |
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| Archimedean Solids (a.k.a. semiregular solids - different types of faces, but every vertex is the same) | |||||||||
| Truncated Tetrahedron Triangles in place of Hexagons ![]() |
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Cuboctahedron![]() |
Truncated Octahedron Triangles in place of Hexagons ![]() |
Truncated Cube Octagons not available ![]() |
Rhombicuboctahedron![]() |
Truncated Cuboctahedron Octagons not available ![]() |
Snub Cuboctahedron Click here for left-handed version. ![]() |
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Icosidodecahedron![]() |
Truncated Icosahedron Triangles in place of Hexagons ![]() |
Truncated Dodecahedron Decagons not available ![]() |
Rhombicosidodecahedron![]() |
Truncated Icosidodecahedron Decagons not available ![]() |
Snub Icosidodecahedron Click here for left-handed version. ![]() |
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| Prisms and Antiprisms (an infinite set of solids - here are the ones you can make with JOVO) | |||||||||
Triangular Prism![]() |
Square Prism![]() |
Pentagonal Prism![]() |
Hexagonal Prism Triangles in place of Hexagons ![]() |
Dodecagonal Prism Tri & Squ in place of Dodecagons ![]() |
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Triangular Antiprism![]() |
Square Antiprism![]() |
Pentagonal Antiprism![]() |
Hexagonal Antiprism Triangles in place of Hexagons ![]() |
Dodecagonal Antiprism Tri & Squ in place of Dodecagons ![]() |
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| Johnson Solids (ALL the convex solids not already mentioned above) | |||||||||
| (Triangular Pyramid = Tetrahedron) | Elongated Triangular Pyramid![]() |
(Gyroelongated Triangular Pyramid has adjacent coplanar faces) | Triangular Dipyramid![]() |
Elongated Triangular Dipyramid![]() |
(Gyroelongated Triangular Dipyramid has adjacent coplanar faces) | ||||
Square Pyramid![]() |
Elongated Square Pyramid![]() |
Gyroelongated Square Pyramid![]() |
(Square Diyramid = Octahedron) | Elongated Square Dipyramid![]() |
Gyroelongated Square Dipyramid![]() |
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| Pentagonal Pyramid Face angles too sharp to close ![]() |
Elongated Pentagonal Pyramid![]() |
Gyroelongated Pent. Pyramid (a.k.a. diminished icosahedron) ![]() |
Pentagonal Dipyramid![]() |
Elongated Pentagonal Dipyramid![]() |
(Gyroelongated Pentagonal Dipyramid = Icosahedron) | ||||
| Triangular Cupola Triangles in place of Hexagons ![]() |
Elongated Triangular Cupola Triangles in place of Hexagons ![]() |
Gyroelongated Triangular Cupola Triangles in place of Hexagons ![]() |
Triangular Orthobicupola![]() |
(Triangular Gyrobicoupola = Cuboctahedron) | Elongated Tri. Orthobicupola![]() |
Elongated Tri. Gyrobicupola![]() |
Gyroelongated Tri. Bicupola Click here for left-handed vers. ![]() |
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| Square Cupola Octagons not available ![]() |
Elongated Square Cupola Octagons not available ![]() |
Gyreoelongated Square Cupola Octagons not available ![]() |
Square Orthobicupola![]() |
Square Gyrobicupola![]() |
(Elongated Square Orthobicupola = rhombicuboctahedron) | Elongated Squ. Gyrobicupola![]() |
Gyroelongated Squ. Bicupola Click here for left-handed vers. ![]() |
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| Pentagonal Cupola Decagons not available ![]() |
Elongated Pentagonal Cupola Decagons not available ![]() |
Gyroelongated Pent. Cupola Decagons not available ![]() |
Pentagonal Orthobicupola![]() |
Pentagonal Gyrobicupola![]() |
Elongated Pent. Orthobicupola![]() |
Elongated Pent. Gyrobicupola![]() |
Gyroelongated Pent. Bicupola Click here for left-handed vers. ![]() |
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| Pentagonal Rotunda Decagons not available ![]() |
Elongated Pentagonal Rotunda Decagons not available ![]() |
Gyroelongated Pent. Rotunda Decagons not available ![]() |
Pentagonal Orthobirotunda![]() |
(Pentagonal Gyrobirotunda = Icosidodecahedron) | Elongated Pent. Orthobirotunda![]() |
Elongated Pent. Gyrobirotunda![]() |
Gyroelongated Pent. Birotunda Click here for left-handed vers. ![]() |
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|   |   |   | Pentagonal Orthocupolarotunda![]() |
Pentagonal Gyrocupolarotunda![]() |
Elong. Pent. Orthocupolarotunda![]() |
Elong. Pent. Gyrocupolarotunda![]() |
Gyroelong. Pent. Cupolarotunda Click here for left-handed vers. ![]() |
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Gyrobifastigium![]() |
Augmented Triangular Prism![]() |
Biaugmented Triangular Prism![]() |
Triaugmented Triangular Prism![]() |
  | Augmented Pentagonal Prism![]() |
Biaugmented Pentagonal Prism![]() |
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| Augmented Hexagonal Prism Triangles in place of Hexagons ![]() |
Parabiaugmented Hex. Prism Triangles in place of Hexagons ![]() |
Metabiaugmented Hex. Prism Triangles in place of Hexagons ![]() |
Triaugmented Hexagonal Prism Triangles in place of Hexagons ![]() |
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Augmented Dodecahedron![]() |
Metabiaugmented Dodecahedron![]() |
Parabiaugmented Dodecahedron![]() |
Triaugmented Dodecahedron![]() |
  | Metabidiminished Icosahedron![]() |
Tridiminished Icosahedron![]() |
Autmented Tridim. Icosahedron![]() |
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| Augmented Trunc. Tetrahedron Triangles in place of Hexagons ![]() |
  |   |   |   | Augmented Truncated Cube Octagons not available ![]() |
Biaugmented Truncated Cube Octagons not available ![]() |
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| Aug. Trunc. Dodecahedron Decagons not available ![]() |
Parabiaug. Trunc. Dodecahedron Decagons not available ![]() |
Metabiaug. Trunc. Dodeca. Decagons not available ![]() |
Triaug. Trunc. Dodecahedron Decagons not available ![]() |
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| Remember that models with decagons can often be approximated by excavating pentagonal cupolas, like this for J83 | |||||||||
Gyrate Rhombicosidodecahedron![]() |
Paragyrate Rhombicosidodeca.![]() |
Metagyrate Rhombicosidodeca.![]() |
Trigyrate Rhombicosidodeca.![]() |
Diminished Rhombicosidodeca. Decagons not available ![]() |
Paragyr. Dim. Rhombicosidod. Decagons not available ![]() |
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| Metagyr. Dim. Rhombicosidod. Decagons not available ![]() |
Bigyr. Dim. Rhombicosidod. Decagons not available ![]() |
Parabidim. Rhombicosidodeca. Decagons not available ![]() |
Metabidim. Rhombicosidodeca. Decagons not available ![]() |
Gyr. Bidim. Rhombicosidod. Decagons not available ![]() |
Tridim. Rhombicosidodahedron Decagons not available ![]() |
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Snub Disphenoid![]() |
Snub Square Antiprism![]() |
Sphenocorona![]() |
Augmented Sphenocorona![]() |
Sphenomegacorona![]() |
Hebesphenomegacorona![]() |
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Disphenocingulum![]() |
Bilunabirotunda![]() |
Triangular Hebesphenorotunda Triangles in place of Hexagons ![]() |
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| Non-Convex Polyhedra (some adjacent faces are coplanar, or the angles between the faces are inward instead of outward) | |||||||||
| Chiral (left-handed and right-handed versions) | |||||||||
| Pyramidal Symmetry (one rotational axis, has a different top and bottom) | |||||||||
| Prismatic Symmetry (one rotational axis, top and bottom are the same) | |||||||||
| Tetrahedral Symmetry (four 3-fold rotational axes, three 2-fold rotational axes) (some of these have higher symmetry, but are the tetrahedral equivalent of another model.) | |||||||||
| Stretched E3 (= B4) with Dents (Toroidal Model) ![]() |
24-sided Deltahedron Tetra. variant of deltathera below ![]() |
Partial Tetrahedron Made from Octa. and Tetra. ![]() |
Stretched Icosahedron![]() |
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| Octahedral Symmetry (three 4-fold rotational axes, four 3-fold rotational axes and 6 2-fold rotational axes) | |||||||||
Stretched E4 with Dents![]() |
48-sided Deltahedron![]() |
Out-folded Catalog Model![]() |
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| Icosahedral Symmetry (six 5-fold rotational axes, ten 3-fold rotational axes and 15 2-fold rotational axes) (some of these have lower symmetry, but are based on an icosahedral model.) | |||||||||
Stretched E5 with Dents![]() |
120-sided Deltahedron![]() |
E5-4H3![]() |
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| Toroidal Polyhedra (models with "handles" - these are all non-convex figures as well) | |||||||||
| Pyramidal Symmetry (one rotational axis, has a different top and bottom) | |||||||||
Pyramids and Prisms![]() |
Cups and Prisms![]() |
Rotunda - Cup and Antiprism![]() |
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| Prismatic Symmetry (one rotational axis, top and bottom are the same) | |||||||||
Pyramids and Prisms![]() |
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| Tetrahedral Symmetry (four 3-fold rotational axes, three 2-fold rotational axes) | |||||||||
| Octahedral Symmetry (three 4-fold rotational axes, four 3-fold rotational axes and 6 2-fold rotational axes) | |||||||||
| Icosahedral Symmetry (six 5-fold rotational axes, ten 3-fold rotational axes and 15 2-fold rotational axes) | |||||||||
Thanks to Robert Webb for his very cool "Stella" program. I have used it extensively to generate VRML files for my site. It is a great tool for rapid exploration of augmentations and excavations of polyhedra (among other things).
Thanks also to Melinda Green and Don Hatch for their excellent Tyler Web Application. This free web tool lets you do great flat designs with polygons in just about any arrangement.
All pages on this site were written in Microsoft's Notepad, using Microsoft Paint and IrfanView for image editing. For more details, see my Help Page