# Elements of Architecture

## Geometric Systems in Architecture

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## Lesson 4: Geometric Solids

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Objective:
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Familiarize students with specific geometric solids; Students will construct a cube, tetrahedron, and octahedron.

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Cube
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: Construct a cube by copying the sketch below. Cut on the solid lines and fold on the dotted lines. Tape tabs to create a cube. (each square is 3” x 3”)

(figure available in print form)

a) A cube has ___________ vertices.

b) A cube has ___________ edges.

c) The edge is the intersection of ______________ faces.

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Tetrahedron
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: Construct an equilateral triangle by;

(figure available in print form)

- 1) Draw a line segment 3 inches long.
- (figure available in print form)
- 2) Set the compass by putting the point at one end of the line segment (x) and the pencil at the other end (y).
- 3) Swing the compass from the x vertex and make an arc. Place the point on the y vertex and repeat the motion. Draw segments xz and yz.

Use this model to draw the pattern below. Cut on the solid lines and fold on the dotted lines, then tape the tabs to form a tetrahedron.

(figure available in print form)

Complete: | A tetrahedron has ______________ faces. |

A tetrahedron has ______________ edges. | |

A tetrahedron has ______________ vertices. | |

_____________ faces intersect at each vertex. |

(figure available in print form)

An octahedron has _______________ faces.

An octahedron has _______________ edges.

An octahedron has _______________ vertices.

Is there any pattern to the number of faces, edges, and vertices of these figures?

Figure | sides | faces | edges |

Cube

Octahedron

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Objective:
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Demonstrate the shape created when 5 equilateral triangles are attached around a center point.

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Instructions:
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Cut along solid lines and fold along the dotted lines, then secure the tabs. The resulting figure will be a pentagonal cup shape.

(figure available in print form)

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Objective:
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Demonstrate the shape created when 7 equilateral triangles are attached about a center point. The resulting pattern will be an undulating saddle.

(figure available in print form)

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Objective:
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Construct a triangular prism.

(figure available in print form)

Count the number of vertices _________________.

Count the number of edges ____________________.

Count the number of faces ____________________.

Name the kinds of faces ______________________.

Extra: Build an icosahedron (a 20 sided regular figure)

(figure available in print form)

Does the formula demonstrated with cubes, tetrahedrons, and octahedrons hold true for triangular prisms? for icosahedrons?