Symmetry Orbits

1. Front Matter

   Pages i-vii

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2. Introduction

   1. Introduction

      • Hugo F. Verheyen

      Pages 1-8

3. Realization of Symmetry Groups

   1. Front Matter

      Pages 9-9

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   2. Groups of Isometries

      • Hugo F. Verheyen

      Pages 11-66

   3. Symmetry Action

      • Hugo F. Verheyen

      Pages 67-79

   4. Orbit Systems

      • Hugo F. Verheyen

      Pages 81-91

4. Compounds of Cubes

   1. Front Matter

      Pages 93-93

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   2. Classification of the Finite Compounds of Cubes

      • Hugo F. Verheyen

      Pages 95-159

   3. Stability of Subcompounds

      • Hugo F. Verheyen

      Pages 161-194

   4. Higher Descriptives

      • Hugo F. Verheyen

      Pages 195-200

   5. Assembling Models

      • Hugo F. Verheyen

      Pages 201-221

5. Back Matter

   Pages 223-236

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In a broad sense design science is the grammar of a language of images rather than of words. Modem communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. Inter­ national traffic signs use international image symbols which are not An image language differs specific to any particular verbal language. from a verbal one in that the latter uses a linear string of symbols, whereas the former is multidimensional. Architectural renderings commonly show projections onto three mutually perpendicular planes, or consist of cross sections at different altitudes capable of being stacked and representing different floor plans. Such renderings make it difficult to imagine buildings compris­ ing ramps and other features which disguise the separation between and consequently limit the creative process of the architect. floors, Analogously, we tend to analyze natural structures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures.

• Symmetry group
• communication
• design
• rendering
• stability

• Antwerpen, Belgium

  Hugo F. Verheyen

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