ホモテナシ

The document above states that the first attempt at classifying 薄茶器 is by 武野紹鴎:

1. 頭切(ずんぎり) or 寸切 (cut off head), of which the 金輪寺(きんりんじ) is a famous example.
2. 臨器(のぞき), which belongs to a family of old, Chinese-style medicine containers used in temples. Related terms are the 西大寺茶器 and 薬器.
3. 帽子 (hat, so it has a protruding lid)
4. 飯器 (rice vessel

• I think Burkus somewhere explains that the 棗 is modeled after the 茶入's 挽家:

• 仙叟 has a set of 12 favourites, as well as 井伊直弼. 仙叟's list:
  1. 再来棗(さいらい)
  2. 尻張棗(しりばり) (swollen bottom)
  3. 茶合(ちゃごう)
  4. 大棗
  5. 茶桶 (tea bucket)
  6. 面中次(めん) (beveled)
  7. 中棗
  8. 鶯棗(うぐいす)
  9. 碁笥棗(ごけ) (a Go stone bucket)
  10. 平棗
  11. 小棗
  12. 一服入棗 (one serving)

Here, we have a whole bunch of items, some with more established traditions:

• 四滴茶入 (misleadingly named, since the lid still goes to 6 o'clock). For those, HS showed me a little dance to remember their four shapes.
  • Among those is the handled つるつき. Here the 茶杓 goes throug the handle. For purifying, first clean the front, then turn CW 90° to clean the back (both straight).
  • For the 割蓋　手桶 that I have, KR25 and I conjecture: Clean like above, either turning back before setting down, or turning as you set it down. For scooping, however, turn CCW by 90°, flip the lid of the front (now to the R) and put it on the other side of the handle. For presenting it during 拝見 and during 拝見 itself, also rest the front lid on the back side.
• 中次
• 吹雪, named so because top and bottom look the same (like when you're in a snow storm).
• 金輪寺
• …