5L-1 Notes on the Pentalateral

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

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

Pentalateral items or 5L-items arise from different sources:

• The items denoted with prefix “5L-s-” are the items that are specific for the Pentalateral and cannot be generalized for n>5.
• The items denoted with prefix “5L-n-” are the items that occur for the Pentalateral and can be generalized for n>5 as well.
• The items denoted with prefix “5L-o-” are the items that occur for the Pentalateral and can be generalized for n>5 as well, where n is odd.
• 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 Pentalaterals spanned around a conic. See note below.

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

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

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