5P-1 Notes on the Pentangle

A Pentangle is defined in EPG as a configuration of 5 random unordered points with no relationship at all. As a reference system there are no lines involved. Also can be spoken about a 5-Point or a 5P. Items relating to the Pentangle are prefixed with “5P-”.

Pentangles are other things than Pentalaterals (see 5L-1) or Pentagons (see 5G-1).

Pentangle items or 5P-items arise from different sources:

1. The items denoted with prefix “5P-s-” are the items that are specific for the Pentangle and cannot be generalized for n>5.
2. The items denoted with prefix “5P-n-” are the items that occur for the Pentangle and can be generalized for n>5 as well.
3. The items denoted with prefix “5P-o-” are the items that occur for the Pentangle and can be generalized for n>5 as well, where n is odd.
4. The items coming forward from items with prefix “CO-“ being conical items. These specific 5P-items also exist at a higher level, namely at the conical level, due to the fact they are identical for all pentangles spanned in a conic. See note below.

Note: By describing Pentangle items, there will be an overlap with conical items. Nevertheless they will also be described as 5P-items because often they can be derived from the properties of a Quadrangle and often the items are so embedded with other Pentangle items that they can be considered as Pentangle items as well.

However when 5P-items also are conical ones, it will be noted in the description of the 5P-item.

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