JovoToys
    Jovo Click 'N Construct

    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
     Archimedean Solids (a.k.a. semiregular solids - different types of faces, but every vertex is the same)
       Truncated Tetrahedron
    Triangles in place of Hexagons
       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.
       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.
     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
       Triangular Antiprism
     
    Square Antiprism
     
    Pentagonal Antiprism
     
    Hexagonal Antiprism
    Triangles in place of Hexagons
    Dodecagonal Antiprism
    Tri & Squ in place of Dodecagons
     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
       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.
       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.
       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.
       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.
             Pentagonal Orthocupolarotunda
     
    Pentagonal Gyrocupolarotunda
     
    Elong. Pent. Orthocupolarotunda
     
    Elong. Pent. Gyrocupolarotunda
     
    Gyroelong. Pent. Cupolarotunda
    Click here for left-handed vers.
       Gyrobifastigium
    Augmented Triangular Prism
    Biaugmented Triangular Prism
    Triaugmented Triangular Prism
      Augmented Pentagonal Prism
    Biaugmented Pentagonal Prism
       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
       Augmented Dodecahedron
    Metabiaugmented Dodecahedron
    Parabiaugmented Dodecahedron
    Triaugmented Dodecahedron
      Metabidiminished Icosahedron
    Tridiminished Icosahedron
    Autmented Tridim. Icosahedron
       Augmented Trunc. Tetrahedron
    Triangles in place of Hexagons
            Augmented Truncated Cube
    Octagons not available
    Biaugmented Truncated Cube
    Octagons not available
       Aug. Trunc. Dodecahedron
    Decagons not available
    Parabiaug. Trunc. Dodecahedron
    Decagons not available
    Metabiaug. Trunc. Dodeca.
    Decagons not available
    Triaug. Trunc. Dodecahedron
    Decagons not available
      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
       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
       Snub Disphenoid
    Snub Square Antiprism
    Sphenocorona
    Augmented Sphenocorona
    Sphenomegacorona
    Hebesphenomegacorona
       Disphenocingulum
     
    Bilunabirotunda
     
    Triangular Hebesphenorotunda
    Triangles in place of Hexagons
    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
     
     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
     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
    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
     Prismatic Symmetry (one rotational axis, top and bottom are the same)
       Pyramids and Prisms
     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)




    Jump straight to Pictures of Models, Mathematical Models, Creative Models or Lesson Planning,
    Go back to the Jovo Toys Main Page
    Or go buy some more Jovo Toys on the Ordering Page

    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



    Link to this page as http://www.JovoToys.com/JovoMathematical.html
    Alexander's Polyhedra, (c) 1998-2008, Alex Doskey