986.300 Minimum-Maximum System Limits

986.301 Consideration 11: Maximum-limit Case

986.302 The explorer gains assurance by discovering the relevant minimum-maximum limit casesthe min-max limits of the variablesof the system under consideration.

986.303 For instance, we have learned through experimental evidence, the cosmic hierarchy of primitive polyhedra has a limit set of seven axes of great-circle symmetries and spinnabilities. They are the 3, 4, 6 (VE), 12, 10, 15, 6 (icosa) great-circle-spinnable systems. (See Table 986.304 and Sec. 1040.) Within that inherently limited hierarchy of seven symmetries, the triacontahedron, with its 15 different great circles’ self-hemispherings and 120 triangular interconfigurings, produces the maximum-limit number of identical polyhedral surface self-facetings of all great-circle systems in Universe (Sec. 400).

Table 986.304: Limit Set of Seven Axes of Spinnability

+:-------------------+:-----------------+
| Generalized Set | |
+--------------------+------------------+
| of All Symmetrical | Spinnable System |
+--------------------+------------------+
| Systems: | Great Circles: |
+--------------------+------------------+
| #1 | > 3 |
+--------------------+------------------+
| #2 | > 4 |
+--------------------+------------------+
| #3 | > 6 (VE) |
+--------------------+------------------+
| #4 | > 12 |
+--------------------+------------------+
| #5 | > 10 |
+--------------------+------------------+
| #6 | > 15 |
+--------------------+------------------+
| #7 | > 6 (icosa) |
+--------------------+------------------+

(Compare Secs. 1041.01 and 1042.05.)