Describe these houses in terms of 2-D shapes and 3D objects. Use words such as: 3D objects, edges, faces, 2-D shapes, vertices.

Here's a description of the houses in terms of 2-D shapes and 3D objects, along with the number of faces, edges, and vertices for their components.

House 1 (Top Left - Cylindrical base, Conical roof)

• 3D objects: This house is composed of a cylinder (base) and a cone (roof).
• 2-D shapes: The cylinder has two circular faces and one rectangular face (when unrolled). The cone has one circular face and one sector-shaped face (when unrolled).
• Faces: The cylinder has 3 faces; the cone has 2 faces.
• Edges: The cylinder has 2 circular edges; the cone has 1 circular edge.
• Vertices: The cylinder has 0 vertices; the cone has 1 vertex (apex).

House 2 (Top Right - Cylindrical base, Octagonal Pyramid roof)

• 3D objects: This house is composed of a cylinder (base) and an octagonal pyramid (roof).
• 2-D shapes: The cylinder has two circular faces and one rectangular face (when unrolled). The octagonal pyramid has one octagonal base and eight triangular faces.
• Faces: The cylinder has 3 faces; the octagonal pyramid has 9 faces.
• Edges: The cylinder has 2 circular edges; the octagonal pyramid has 16 edges.
• Vertices: The cylinder has 0 vertices; the octagonal pyramid has 9 vertices.

House 3 & 4 (Middle and Bottom - Rectangular Prism base, Triangular Prism roof)

• 3D objects: Each of these houses is composed of a rectangular prism (base) and a triangular prism (roof).
• 2-D shapes: The rectangular prism has six rectangular faces. The triangular prism has two triangular faces and three rectangular faces.
• Faces: The rectangular prism has 6 faces; the triangular prism has 5 faces.
• Edges: The rectangular prism has 12 edges; the triangular prism has 9 edges.
• Vertices: The rectangular prism has 8 vertices; the triangular prism has 6 vertices.

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Designing a house:
To determine how many different houses can be designed, we identify the unique types of 3D objects available for wall structures (bases) and roof structures.

• Unique Wall Structure Types:
  1. Rectangular Prism (including the open one)
  2. Triangular Prism
• Unique Roof Structure Types:
  1. Square Pyramid
  2. Rectangular Prism
  3. Triangular Prism

The number of different houses is the product of the number of unique wall structure types and the number of unique roof structure types.
Number of different houses = (Number of wall structure types) $\times$ (Number of roof structure types)
Number of different houses = $2 \times 3 = 6$

You can design $\boxed{\textbf{6}}$ different houses.