Did you know that a soccer ball is very similar to a truncated icosahedron? Both have 32 faces, but while a truncated icosahedron is made up solely of flat hexagons, a traditional soccer ball has 12 pentagons and 20 hexagons, each curved to help create a ball that is generally spherical. In fact, the shape of a soccer ball is one of the most mathematically intriguing issues in soccer today. If you find this all fascinating, then you will love this app.
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App Overview
iCrosss is a reference app of different polyhedrons. It has about 50 different polyhedrons which you can choose to explore and modify.
One of the most challenging parts to teaching and exploring solid geometry, is the ability to picture and draw the different shapes. This is especially true as the number of faces, vertices, and edges increase. This app does a wonderful job helping learners expand their understanding by providing a clear and easy-to-manipulate model of the different solids.
Capabilities:
- Rotate and spin using your fingers
- Add vertices on the faces to build a cross section
- View polyhedron in different modes
- Can break the polyhedra apart at the cross section
- Print different views of the polyhedra
- Click on the share button to find out information about the polyhedron.
- Information includes:
- General description
- Number of vertices
- Number of edges
- Number of faces
- Formulas which deal with different aspects of the shape
Polyhedrons:
- Platonic Solids:
- Tetrahedron
- Cube
- Octahedron
- Dodecahedron
- Icosahedron
- Archimedean Polyhedra:
- Truncated Tetrahedron
- Truncated Cube
- Truncated Octahedron
- Truncated Dodecahedron
- Truncated Icosahedron
- Cuboctahedron
- Icosidodecahedron
- Rhombicuboctahedron
- Truncated Cuboctahedron
- Truncated Icosidodecahedron
- Snub Cuboctahedron
- RhombIcosiDodecahedron
- Snub IcosiDodecahedron
- Pyramids:
- Square Pyramid
- Pentagonal Pyramid
- Triangular Dipyramid
- Pentagonal Dipyramid
- Prisms:
- Triangular Prism
- Pentagonal Prism
- Hexagonal Prism
- Heptagonal Prism
- Octagonal Prism
- Enneagonal Prism
- Decagonal Prism
- Anti-Prisms:
- Square Antiprism
- Pentagonal Antiprism
- Hexagonal Antiprism
- Heptagonal Antiprism
- Octagonal Antiprism
- Enneagonal Antiprism
- Decagonal Antiprism
- Archimedean Duals:
- Triakis Tetrahedron
- Triakis Octahedron
- Triakis Icosahedron
- Tetrakis Hexahedron
- Rhombic Dodecahedron
- Rhombic Triacontahedron
- Trapezoidal Icositetrahedron
- Trapezoidal Hexecontahedron
- Pentagonal Icositetrahedron
- Pentakis dodecahedron
- Pentagonal Hexecontahedron
- Disdyakis Dodecahedron
- Disdyakis Triacontahedron
Instructional Ideas
- Create an Internet treasure hunt looking for unique buildings or sculptures that are, or include, a polyhedra
- Have learners explore the historical significance of different solids.
- A creative, reliable reference tool for learners
Classroom Considerations
- Useful for projecting different solids for the whole class to explore
Pros
- Helps with understanding and visualizing spacial relationships
Cons
- Doesn't support cylinders, cones, or shapes with a circular cross section