Architectural Informatics 2 
AutoCAD 3D/1 
Digital Representation 

Create the following vaults and spires over 4×4×3 sized box elements.
(source)

1. Cross and cloister vaults, sail vault, dome on pendentives
Create a cross vault as the union of two semicylinders and a cloister vault as the intersection of two semicylinders.
Create a sail vault as the intersection of a box and a sphere. Create the dome on pendentives by decreasing the height of the box and placing a hemisphere on the top of the resulting pendentives.
2. Crossgabled roof, pyramid, basetruncated pyramid
Create a crossgabled roof as the union of two prisms of regular triangle base and pyramid as the intersection of two prisms.
Create a rotated basetruncated pyramid as the intersection of a box and a pyramid.
3. Composite spire
Create a truncated pyramid as the intersection of two pyramids of square base.
Create a spire as the union of this truncated pyramid and a pyramid of regular octogon base.
Further examples:
SpirePolyhedra,
Journal for Geometry and Graphics,
11/1, 111–126,
2007.
2009.
Strommer L.
• BME Építészeti Ábrázolás Tanszék