Shards

So I'll be using this page as a sandbox for my Cosmere works. First, I'll counting how many possible combinations of things you could derive from the sixteen Shards of Adonalsium.

=Forms of Shardic Investiture=
 * God-Metal: Investiture in the form of solid matter
 * Perpendicularity-Liquid: Investiture in the form of liquid matter
 * Light: Investiture manifest as pure energy
 * Tone: Frequency attuned to a Shard's Investiture

=Metallic-Arts= Usable metals and what we know
 * 16 base-metals
 * 8 chemical-element metals: Iron, Tin, Zinc, Copper, Aluminum, Chromium, Gold, Cadmium
 * 8 alloys of those metals: Steel, Pewter, Brass, Bronze, Duralumin, Nicrosil, Electrum, Bendalloy
 * 16 God-Metals
 * Lerasium: God-Metal of Preservation, Shard primarily connected to Allomancy
 * Atium: God-Metal of Ruin, Shard secondarily connected to Allomancy

Known statements about the Metallic-Arts
 * Each metal can be used for Allomancy, Feruchemy, and Hemalurgy

=Shardic synthesis= Individual [16 total]
 * 1
 * 2
 * 3
 * 4
 * 5
 * 6
 * 7
 * 8
 * 9
 * 10
 * 11
 * 12
 * 13
 * 14
 * 15
 * 16

Duality (2 of 16) [120 total]
 * 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12, 1/13, 1/14, 1/15, 1/16
 * 2/3, 2/4, 2/5, 2/6, 2/7, 2/8, 2/9, 2/10, 2/11, 2/12, 2/13, 2/14, 2/15, 2/16
 * 3/4, 3/5, 3/6, 3/7, 3/8, 3/9, 3/10, 3/11, 3/12, 3/13, 3/14, 3/15, 3/16
 * 4/5, 4/6, 4/7, 4/8, 4/9, 4/10, 4/11, 4/12, 4/13, 4/14, 4/15, 4/16
 * 5/6, 5/7, 5/8, 5/9, 5/10, 5/11, 5/12, 5/13, 5/14, 5/15, 5/16
 * 6/7, 6/8, 6/9, 6/10, 6/11, 6/12, 6/13, 6/14, 6/15, 6/16
 * 7/8, 7/9, 7/10, 7/11, 7/12, 7/13, 7/14, 7/15, 7/16
 * 8/9, 8/10, 8/11, 8/12, 8/13, 8/14, 8/15, 8/16
 * 9/10, 9/11, 9/12, 9/13, 9/14, 9/15, 9/16
 * 10/11, 10/12, 10/13, 10/14, 10/15, 10/16
 * 11/12, 11/13, 11/14, 11/15, 11/16
 * 12/13, 12/14, 12/15, 12/16
 * 13/14, 13/15, 13/16
 * 14/15, 14/16
 * 15/16

 (3 of 16) [ total]

 (4 of 16) [ total]

 (5 of 16) [ total]

 (6 of 16) [ total]

 (7 of 16) [ total]

Reforming (8 of 16) [ total]

Advancing (9 of 16) [ total]

 (10 of 16) [ total]

 (11 of 16) [ total]

 (12 of 16) [ total]

 (13 of 16) [ total]

Super-conglomeration (14 of 16) [120 total]

Near-complete (15 of 16) [16 total]
 * 1-15
 * 2-16
 * 1+3-16
 * 1+2+4-16
 * 1-3+5-16
 * 1-4+6-16
 * 1-5+7-16
 * 1-6+8-16
 * 1-7+9-16
 * 1-8+10-16
 * 1-9+11-16
 * 1-10+12-16
 * 1-11+13-16
 * 1-12+14-16
 * 1-13+15+16
 * 1-14+16

Whole (all 16) [1 total]
 * 1-16