Reciprocating the second figure results in the original. Geometrical reciprocation about some sphere twins every ordinary polyhedron with a reciprocal figure. Such an abstract polytope may be distinguished from its geometrical form: any given abstract polyhedron may be realized as a wide variety of geometric polyhedra, all having the same underlying form. A polygon is bounbded by a chain of ditela, a polyhedron by a surface constructed of polygons, and so on.Įvery polyhedron has an abstract combinatorial structure which describes the connectivity or incidences of its elements. It is bounded by two vertex points, its sub-dimensional elements. Next up, in 1 dimension, is the line segment or ditelon.

The simplest polytope, of 0 dimension, is a point. We understand a polytope to be made up of sub-polytopes or subtopes, also known as its elements. It is worth summarising some of the more important ideas here. Some broad problem areas include:Īny coherent understanding of polyhedra and polytopes must take on board a number of theoretical advances which have been made over the centuries. Conversely, the student of higher polytopes will readily be able to extend the principles described.ĭespite over 2,000 years of academic study, mathematicians have yet toĬome up with a satisfactory understanding of certain properties of the

For the reader concerned only with the familiar three dimensions, where the word 'polytope' is encountered, you may substitute 'polyhedron' with no loss of rigour. The bottom-line is that changing the environment that we currently operate in is necessary if we need positive results from our efforts.The ideas presented in this essay are generally applicabe to higher polytopes, although the focus here is on three-dimensional polyhedra. However, I understand that an all-inclusive discussion is important for such changes to be implemented. Such actions should include bringing forward alternative recommendations or supporting the recommendations that I have proposed. A number of students have already endorsed these measures. I would like to call upon every concerned student to analyze the problems that we have and take appropriate actions. What we do with what we have at the moment will determine the outcome of our lives. I believe that this measure will go a long way in ensuring that there is peace of mind for those who wish to work in silence. The fine charged will be agreed upon collectively by all the students involved. I would like to propose a fine for persons who disturb the peace of the studio. This is probably because some of us fail to acknowledge that the work of their colleagues is just as important as their own. However, during certain moments we may not have the silence that we yearn for. Improvement of our work requires focus at all times. Further, noise has been a menace at certain points in the studio. Addressing this concern will not only improve the tidiness of the workplace but also the security of our belongings and our personal safety.

On many occasions, we find personal belongings left unattended to by their owners hence making the place untidy and at the same time endangering the physical safety of some of us. Everyone needs to keep their personal belongings close to them. In that regard, we should all take responsibility for where we leave our personal belongings around the studio. This is not only required of the cleaning staff but also the students. Additionally, I feel that the level of tidiness in the studio needs to be improved. This action will also improve the overall outlook of the room and make it more presentable to both students and the instructor. The furniture and equipment should be rearranged to suit the structure of the room. We can achieve this by pulling some of the furniture together to create wider space for movement. This calls for the rearrangement of the working space to create room for movement in the studio. Congestion has on many occasions led to injury to students while they are working. I have observed that the working space is limited because of the arrangement of furniture and equipment. The space in the studio needs to be reshuffled.

Tidiness essay