I have suggested a classification for the shells of heptiamond shapes with maximal symmetry. It uses Latin binominal names in the fashion of Linnaeus' taxonomy of nature. Each of the Latin names in the table below is clickable and directs to the database of shapes. Gender of nouns is indicated with m. (masculine), f. (feminine) and n. (neuter). Genitive ending s indicated as well.
| A | |
| Arx, cis | f. Fortress. |
| Arx Dentata | Fortress with teeth. |
| Arx Duplex | Double fortress. |
| Arx Lata | Wide fortress. |
| Arx Latior | Wider fortress. |
| Arx Simplex | Plain fortress. |
| B | |
| Bifidus, i | m. Bifid, divided in two two lobes. |
| Bifidus Duplex | Double bifid. |
| Bifidus Explosus | Exploded bifid. |
| Bifidus Simplex | Plain bifid. |
| Bifidus Triplex | Triple bifid. |
| C | |
| Chrysanthemum, i | n. Chrysanthemum. |
| Chrysanthemum Simplex | Plain chrysanthemum. |
| Corona, ae | f. Crown. |
| Corona Alta | High crown. |
| Corona Lata | Wide crown. |
| Corona Latior | Wider crown. |
| Corona Simplex | Plain crown. |
| F | |
| Floccus Nivalis | Snowflake. |
| Flos | m. Flower. |
| Flos Arcis | Flower of the fortress. |
| Flos Simplex | Plain flower. |
| Flos Spinatus | Thorny flower. |
| H | |
| Heptahexus, i | m. Heptahex, a shape made of seven hexagons. |
| Heptahexus Latior | Wider heptahex. |
| Heptahexus Latus | Wide heptahex. |
| Heptahexus Simplex | Plain heptahex. |
| Heptakaitriacontahexus, i | m. A shape made of 37 hexagons. |
| Heptakaitriacontahexus Simplex | Plain shape of 37 hexagons. |
| Hexagonus, i | m. Hexagon. |
| Hexagonus Eurystomus | Hexagon with wide mouth. |
| Hexagonus Ferox | Ferocious hexagon. |
| Hexagonus Simplex | Plain hexagon. |
| Hexagonus Spinatus | Thorny hexagon. |
| Hexagonus Stenostomus | Hexagon with narrow mouth. |
| Hexagonus Terribilis | Terrible hexagon. |
| N | |
| Nonakaidecahexus, i | m. A shape made of 19 hexagons. |
| Nonakaidecahexus Latus | Wide shape of 19 hexagons. |
| Q | |
| Quarzum, i | n. Quartz. |
| Quarzum Latum | Wide quartz. |
| Quarzum Simplex | Plain quartz. |
| S | |
| Stella, ae | f. Star. |
| Stella Arcis | Star of the fortress. |
| Stella Chrysanthemi | Star of the chrysanthemum. |
| Stella Corrupta | Rotten star. |
| Stella Duplex | Double star. |
| Stella Mammata | Mammary star. |
| Stella Quadruplex | Quadruple star. |
| Stella Simplex | Plain star. |
| Stella Spinata | Thorny star. |
| Stella Terribilis | Terrible star. |
| Stella Tridentata | Star with three teeth. |
| Stella Triplex | Triple star. |
| V | |
| Vulcanus, i | m. Volcano. |
| Vulcanus Corruptus | Rotten volcano. |
| Vulcanus Dentatus | Volcano with teeth. |
| Vulcanus Duplex | Double volcano. |
| Vulcanus Explosus | Exploded volcano. |
| Vulcanus Simplex | Plain volcano. |