Category S19: Octicoes

The octicoes are formed by blending two sets of four ico members on hexagons, so both component types must have ohoes or choes in order to blend. They have 96 vertices and 672 edges. All five symmetries of the tessic family are represented - tessic, demitessic, kitessic, kidemitessic, and tessipyritic. Ico members that can blend are 1 oh, 2 shahoh, 3 huhoh, 4 hohoh, 5 odho, 6 hodho, 7 hoh honho, 8 dod honho, and 9 doh honho (but as compounds of four each). We can represent blending by using the numbers and superscripts for different orientations - for example 22 blends two sets of shahohs in same orientation and 33' blends two sets of huhohs in different orientations, 56⁴ blends a set of odhoes and a set of hodhoes in the fourth orientation. Their verfs are facetings of a compound of two cubes attached at opposite corners rotated 180 degrees. All 84 are legit, no fissaries. They were found in 2021.

Cisblended Octicoes

These six are formed by blending two sets of four ico members in the same orientation. The first four have tessic symmetry and the last two have demitessic symmetry and are the only octicoes with those symmetries. The fourth and last are wild, others are tame. The first two are orientable and the others are not.

S2385. Dethifuge - (DETH ih fyooj / dis32hemifusi64) - cells are 32 sthaps (6/2 ap which is a different variation than the ones in sidtaps, this version can be thought of as a Star of David antiprism) and 32 tohobs (2-oho-blend). This is the 11 blend.

S2386. Dighifuge - (DIJ he fyooj / dis64hemifusi64) - cells are 64 sthaps and 32 dohobs. This is the 22 blend.

S2387. Dicuhfuge - (DI kuh fyooj / discupolihemifusi64) - cells are 64 shrucs (6/2 retrocupola - a 2-thah compound) and 32 tuchobs (2-cho-blend). This is the 33 blend.

S2388. Dicudithefuge - (DI ku DITH e fyooj / discupolidis32hemifusi64) - cells are 32 sthaps, 64 shrucs, and 32 tuchobs. This is the 44 blend.

S2389. Dicudhefut - (di CUDH e fut / discupolidishemifusi32) - cells are 32 shrucs, 16 tohobs, and 16 tuchobs. This is the 55 blend.

S2390. Tetdicudhefut - (TET di CUDH e fut / tetris32discupolidishemifusi32) - cells are 32+32 sthaps, 32 shrucs, 16 tohobs, and 16 tuchobs. This is the 66 blend. Slices of the Cisblended Octicoes

Transblended Octicoes

These twelve are formed by blending two sets of the same 4-ico members but in different orientations. The first two are orientable, the others are not. All are wild except for the seventh one. The sixth and tenth ones have kidemitessic symmetry, the others have tessipyritic symmetry and are the only octicoes that are tessipyritic. For the 5 and 6 blends, the four orientations here are distinct from the orientation of the previous section.

S2391. Ghafutheg - (ga FOO theg / 64hemifusi32hemi64) - cells are 64 octs, 16 tohobs, and 32 ohoes. This is the 11' blend.

S2392. Godthufthog - (god THUF thog / 64dis32hemifusi32hemi64) - cells are 32 sthaps, 64 octs, 16 tohobs, and 32 ohoes. This is the 22' blend.

S2393. Gidtheghafut - (gid THEGG a fut / 64dis32hemi64hemifusi32) - cells are 32 tuthahs (a trip symmetric 2-thah compound), 64 thahs, 16 tuchobs, and 32 choes. This is the 33' blend.

S2394. Digdatheghafut - (DIG da THEGG a fut / dis64dis32hemi64hemifusi32) - cells are 32 tuthahs, 64 octthahs (oct thah combo), 16 tuchobs, and 32 choes. This is the 44' blend.

S2395. Dethfutheg - (DETH foo theg / dis32hemifusi32hemi64) - cells are 32 tuthahs, 16 tuchobs, and 32 ohoes. This is the 55¹ blend.

S2396. Dethfutadhot - (deth FOO ta dhot / dis32hemifusi32dishemi32) - cells are 32+32 thahs, 16 ohochobs, 16 ohoes, and 16 choes. This is the 55² blend.

S2397. Gahfug - (GAH fug / 64hemifusi64) - cells are 64 thahs and 32 ohochobs. This is the 55³ blend.

S2398. Gohgohfut - (GO go fut / 64hemi64hemifusi32) - cells are 64 thahs, 16 tohobs, and 32 choes. This is the 55⁴ blend.

S2399. Dogdeth Futheg - (DOG deth FOO theg / dis64dis32hemifusi32hemi64) - cells are 64 sthaps, 32 tuthahs, 16 tuchobs, and 32 ohoes. This is the 66¹ blend.

S2400. Diddith Futadhot - (DID ith FOO ta dhot / disdis32hemifusi32dishemi32) - cells are 32 sthaps, 32+32 octthahs, 16 ohochobs, 16 ohoes, and 16 choes. This is the 66² blend.

S2401. Ditdaghofug - (DIT da GO fug / dis32dis64hemifusi64) - cells are 32 sthaps, 64 octthahs, and 32 ohochobs. This is the 66³ blend.

S2402. Ditdagohgohfut - (DIT da GO go fut / dis32dis64hemi64hemifusi32) - cells are 32 sthaps, 64 octthahs, 16 tohobs, and 32 choes. This is the 66⁴ blend. Slices of the Transblended Octicos

Tessic Biblended Octicoes

These twelve are formed by blending two sets of icoes with tessic symmetry (1-4) in the list above. The first two are orientable, the others are not. The first, third, and seventh are tame, the others are wild. The ones with a ' mark in their blend representation like 23' have kidemitessic symmetry, the ones without it like 23 have kitessic symmetry and are the only ones with that symmetry.

S2403. Teghifuge - (TEG e fyooj / 32-64hemifusi64) - cells are 32+64 octs and 32 tohobs. This is the 12 blend.

S2404. Tidtid Hathefut - (TID tid HATH e fut / 32dis32dishemi32hemifusi32) - cells are 32 octs, 32 sthaps, 16 tohobs, and 2x16 ohoes. This is the 12' blend.

S2405. Gothifuge - (GOTH ih fyooj / 64-32hemifusi64) - cells are 32 octs, 64 thahs, and 32 ohochobs. This is the 13 blend.

S2406. Ted Thefutadhot - (TED theh FOO ta dhot / 32dis32hemifusi32dishemi32) - cells are 32 thahs, 32 octthahs, 16 ohochobs, 16 ohoes, and 16 choes. This is the 13' blend.

S2407. Gadithafuge - (ga DITH a fyooj / 64dis32hemifusi64) - cells are 64 thahs, 32 sthaps, and 32 ohochobs. This is the 14 blend.

S2408. Tethifutadhot - (TETH e FOO ta dhot / tetris32hemifusi32dishemi32) - cells are 32 octs, 32 thahs, 32 octthahs, 16 ohochobs, 16 ohoes, and 16 choes. This is the 14' blend.

S2409. Kedghifuge - (KEJ e fyooj / chirodis64hemifusi64) - cells are 64 octthahs and 32 ohochobs. This is the 23 blend.

S2410. Dahtatatheft - (dah TAT a theft / dishemi32tetris32hemifusi32) - cells are 32 octs, 32 thahs, 32 octthahs, 16 ohochobs, 16 ohoes, and 16 choes. This is the 23' blend.

S2411. Tadithafuge - (ta DITH a fyooj / 32dis32hemifusi64) - cells are 32 octs, 64 octthahs, and 32 ohochobs. This is the 24 blend.

S2412. Pethifutadhot - (PETH e FOO ta dhot / pentis32hemifusi32dishemi32) - cells are 32 thahs, 32 sthaps, 32 octthahs, 16 ohochobs, 16 ohoes, and 16 choes. This is the 24' blend.

S2413. Todghifuge - (TOJ e fyooj / 32dis64hemifusi64) - cells are 32 octs, 64 tuthahs, and 32 tuchobs. This is the 34 blend.

S2414. Tetdich Futadhot - (TET ditch FOO ta dhot / tris32discupolihemifusi32dishemi32) - cells are 32 thahs, 32 shrucs, 32 octthahs, 16 tuchobs, and 2x16 choes. This is the 34' blend. Slices of the Tessic Biblended Octicoes

Tessic-Demi Blended Octicoes

These 24 are formed by blending one set of tessic icoes with a set of demitessic icoes (5 and 6, aka non-honho ones). They all have kidemitessic symmetry. They are non-orientable. 15⁺, 25⁺, and 35⁺ are tame, the others are wild. Notice the + - superscripts.

S2415. - ( / ) - cells are . This is the 15 blend.

S2416. - ( / ) - cells are . This is the 15⁺ blend.

S2417. - ( / ) - cells are . This is the 15^- blend.

S2418. - ( / ) - cells are . This is the 16 blend.

S2419. - ( / ) - cells are . This is the 16⁺ blend.

S2420. - ( / ) - cells are . This is the 16^- blend.

S2421. - ( / ) - cells are . This is the 25 blend.

S2422. - ( / ) - cells are . This is the 25⁺ blend.

S2423. - ( / ) - cells are . This is the 25^- blend.

S2424. - ( / ) - cells are . This is the 26 blend.

S2425. - ( / ) - cells are . This is the 26⁺ blend.

S2426. - ( / ) - cells are . This is the 26^- blend.

S2427. - ( / ) - cells are . This is the 35 blend.

S2428. - ( / ) - cells are . This is the 35⁺ blend.

S2429. - ( / ) - cells are . This is the 35^- blend.

S2430. - ( / ) - cells are . This is the 36 blend.

S2431. - ( / ) - cells are . This is the 36⁺ blend.

S2432. - ( / ) - cells are . This is the 36^- blend.

S2433. - ( / ) - cells are . This is the 45 blend.

S2434. - ( / ) - cells are . This is the 45⁺ blend.

S2435. - ( / ) - cells are . This is the 45^- blend.

S2436. - ( / ) - cells are . This is the 46 blend.

S2437. - ( / ) - cells are . This is the 46⁺ blend.

S2438. - ( / ) - cells are . This is the 46^- blend.

Tessic-Honho Blended Octicoes

These twelve are formed by blending a sets of tessic icoes with a set of honhoes (7-9). They are wild, non-orientable, and have kidemitessic symmetry.

S2439. - ( / ) - cells are . This is the 17 blend.

S2440. - ( / ) - cells are . This is the 18 blend.

S2441. - ( / ) - cells are . This is the 19 blend.

S2442. - ( / ) - cells are . This is the 27 blend.

S2443. - ( / ) - cells are . This is the 28 blend.

S2444. - ( / ) - cells are . This is the 29 blend.

S2445. - ( / ) - cells are . This is the 37 blend.

S2446. - ( / ) - cells are . This is the 38 blend.

S2447. - ( / ) - cells are . This is the 39 blend.

S2448. - ( / ) - cells are . This is the 47 blend.

S2449. - ( / ) - cells are . This is the 48 blend.

S2450. - ( / ) - cells are . This is the 49 blend.

Demitessic Biblended Octicoes

These 18 are formed by blending two sets of demitessic icoes. They all have kidemitessic symmetry and are wild and non-orientable.

S2451. - ( / ) - cells are . This is the 56¹ blend.

S2452. - ( / ) - cells are . This is the 56² blend.

S2453. - ( / ) - cells are . This is the 56³ blend.

S2454. - ( / ) - cells are . This is the 56⁴ blend.

S2455. - ( / ) - cells are . This is the 56⁵ blend.

S2456. - ( / ) - cells are . This is the 56⁶ blend.

S2457. - ( / ) - cells are . This is the 57¹ blend.

S2458. - ( / ) - cells are . This is the 57² blend.

S2459. - ( / ) - cells are . This is the 58¹ blend.

S2460. - ( / ) - cells are . This is the 58² blend.

S2461. - ( / ) - cells are . This is the 59¹ blend.

S2462. - ( / ) - cells are . This is the 59² blend.

S2463. - ( / ) - cells are . This is the 67¹ blend.

S2464. - ( / ) - cells are . This is the 67² blend.

S2465. - ( / ) - cells are . This is the 68¹ blend.

S2466. - ( / ) - cells are . This is the 68² blend.

S2467. - ( / ) - cells are . This is the 69¹ blend.

S2468. - ( / ) - cells are . This is the 69² blend.

Conjugates

Below shows how these pair up as conjugates.

Conjugates

The following are self conjugates: all.

The following are conjugate pairs: none.

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