Duoprisms (also called double prisms) are the cross products of two polygons, its as though we are multiplying one polygon by another one - this category has an infinite size, here we will list all of them up to the decagonal ones. Convex ones are cross products of two convex polygons, all others are starry. Some duoprisms are cross products of two identical polygons, these have a higher symmetry - since these are like multiplying a polygon to itself, they are actually the square of that polygon - these polygon squares are a subset of the 4-D powertopes as well as their duals. Their verfs are disphenoids and are therefore related to category 7. As N approaches infinity, the N x N (or N

**Triddip** - (TRID dip) trigonal duoprism. Its cells are 6 trips. It has 9 vertices and has triddip symmetry. Symbol = ox ox = ox^{2} = ox^{o'x}. It has 6 pieces with one type.

**Pedip** - (PEE dip) pentagonal duoprism. Its cells are 10 pips. It has 25 vertices and has pedip symmetry. Symbol = o^x o^x = o^x^{2}. It has 10 pieces in one type.

**Hiddip** - (HID dip) hexagonal duoprism. Its cells are 12 hips. It has 36 vertices and has hiddip symmetry (usually has triddip symmetry when found in polytera). Symbol = o* ^{6}*x o

**Hedip** - (HEE dip) heptagonal duoprism. Its cells are 14 heps (heptagon prisms). It has 49 vertices and has hedip symmetry. Symbol = o* ^{7}*x o

**Odip** - (O dip) octagonal duoprism. It has 16 ops. It has 64 vertices and odip symmetry (in polytera, it usually has "squiddip" symmetry (or 4^{2}). Symbol = o* ^{8}*x o

**Edip** - (E dip) enneagonal duoprism. It has 18 eps (enneagon prisms). It has 81 vertices and has edip symmetry. Symbol = o* ^{9}*x o

**Dedip** - (DEE dip) decagonal duoprism. It has 20 dips. It has 100 vertices and has dip symmetry. Symbol = o* ^{10}*x o

**Stardip** - (STAR dip) pentagrammic duoprism (or star duoprism). It has 10 stips. It has 25 vertices and has pedip symmetry. Symbol = o*x o*x = o*x^{2}. It has 20 pieces in one type. This is the square of a star.

**Shedip** - (SHE dip) heptagrammic duoprism. The cells are 14 ships (7/2 prism). It has 49 vertices and has hedip symmetry. Symbol = o* ^{7/2}*x o

**Gishdip** - (GISH dip) great heptagrammic duoprism. The cells are 14 giships (7/3 prism). It has 49 vertices and has hedip symmetry. Symbol = o* ^{7/3}*x o

**Stodip** - (STO dip) octagrammic duoprism. The cells are 16 stops. It has 64 vertices and has odip symmetry. Symbol = o* ^{8/3}*x o

**Stedip** - (STE dip) enneagrammic duoprism. The cells are 18 steps (9/2 prism). It has 81 vertices and has edip symmetry. Symbol = o* ^{9/2}*x o

**Gastedip** - (ga STEE dip) great enneagrammic duoprism. The cells are 18 gisteps (9/4 prism). It has 81 vertices and has edip symmetry. Symbol = o* ^{9/4}*x o

**Stadidip** - (sta DID dip) decagrammic duoprism. The cells are 20 stiddips. It has 100 vertices and has dedip symmetry. Symbol = o* ^{10/3}*x o

**N-Dip** - (IN dip) N-gonal duoprism (N > 2, N is an integer). Cells are 2N N-gonal prisms. It has N^{2} vertices and has N-dip symmetry. Symbol = o* ^{N}*x o

**N/M-Dip** - (NIM dip) M density N-grammic duoprism (N/M > 2, M and N relatively prime). Cells are 2N N/M-prisms. It has N^{2} vertices and has N-dip symmetry. Symbol = o* ^{N/M}*x o

**Thiddip** - (THID dip) trigonal-hexagonal duoprism. Its cells are 6 trips and 3 hips. It has 18 vertices and has trigon x trigon symmetry. Symbol = ox xx. It has nine pieces with two types.

**Tisdip** - (TISS dip) trigonal-square duoprism. Its cells are 4 trips and 3 cubes. It has 12 vertices and has tisdip symmetry. Symbol = ox o'x. It has seven pieces in two types.

**Todip** - (TOE dip) trigonal-octagonal duoprism. Its cells are 8 trips and 3 ops. It has 24 vertices and has tisdip symmetry. Symbol = ox x'x. It has 11 pieces with two types.

**Shiddip** - (SHID dip) square-hexagonal duoprism. Its cells are 6 cubes and 4 hips. It has 24 vertices and has tisdip symmetry. Symbol = xx o'x. It has 10 pieces with two types.

**Hodip** - (HO dip) hexagonal-octagonal duoprism. Its cells are 8 hips and 6 ops. It has 48 vertices and has tisdip symmetry. Symbol = xx x'x. It has 14 pieces with two types.

**Sodip** - (SO dip) square-octagonal duoprism. Its cells are 8 cubes and 4 ops. It has 32 vertices and has square x square (or sisdip) symmetry. Symbol = o'x x'x. It has 12 pieces in two types.

**Tistodip** - (tiss TOE dip) trigonal-octagrammic duoprism. Its cells are 8 trips and 3 stops. It has 24 vertices and has tisdip symmetry. Symbol = ox x"x. It has 19 pieces in two types.

**Histodip** - (hiss TOE dip) hexagonal-octagrammic duoprism. Its cells are 8 trips and 6 stops. It has 48 vertices and has tisdip symmetry. Symbol = xx x"x. It has 22 pieces with two types.

**Sistodip** - (sis TOE dip) square-octagrammic duoprism. Its cells are 8 cubes and 4 stops. It has 32 vertices and has sisdip symmetry. Symbol = o'x x"x. It has 20 pieces with two types.

**Ostodip** - (OSS toe dip) octagon-octagrammic duoprism. Its cells are 8 ops and 8 stops. It has 64 vertices and has sisdip symmetry. Symbol = x'x x"x. It has 24 pieces in two types.

**3,5. Trapedip** - (tra PEE dip) ** 3,7. Theddip** - (THEH dip) ** 3,9. Tedip** - (TEE dip) ** 3,10. Tradedip** - (tra DEE dip)

**4,5. Squipdip** - (SQUIP dip) ** 4,7. Shedip** - (SHE dip) ** 4,9. Sendip** - (SEND dip) ** 4,10. Squadedip** - (skwa DEE dip)

**5,6. Phiddip** - (FID dip) ** 5,7. Pheddip** - (FED dip) ** 5,8. Podip** - (PO dip) ** 5,9. Peendip** - (PEEN dip) ** 5,10. Padedip** - (pa DEE dip)

**6,7. Hahedip** - (ha HEE dip) ** 6,9. Hendip** - (HEND dip) ** 6,10. Hadedip** - (ha DEE dip)

**7,8. Heodip** - (HYO dip) ** 7,9. Heendip** - (HEEN dip) ** 7,10. Hedadip** - (he DAY dip)

**8,9. Oedip** - (OIE dip) ** 8,10. Odedip** - (o DEE dip) ** 9,10. Edidip** - (e DID dip)

**M,N. M,N-Dip** - (em IN dip) - hmmm...we could call these the "emindips"

**3,5/2. Tistadip** - (TISS ta dip) ** 3,10/3. Tistadedip** - (TISS ta DEE dip)

**4,5/2. Sistadip** - (SIS ta dip) ** 4,10/3. Sistadedip** - (SIS ta DEE dip) - *Good name for a female rap star - but then again "Rapstar" would be a good name for the pentagram-rap duoprism*

**5,5/2. Starpedip** - (STAR pe dip) ** 5,8/3. Pistodip** - (PISS toe dip) ** 5,10/3. Pistadedip** - (PISS ta DEE dip)

**6,5/2. Stahdip** - (STAH dip) ** 6,10/3. Histadedip** - (HISS ta DEE dip)

**7,5/2. Stahedip** - (stah HE dip) ** 7,8/3. Hestodip** - (HESS sto dip) ** 7,10/3. Hestadedip** - (HESS ta DEE dip)

**8,5/2. Starodip** - (STARE o dip) ** 8,10/3. Ostadedip** - (OSS ta DEE dip)

**9,5/2. Starendip** - (sta REN dip) ** 9,8/3. Stoendip** - (STOIN dip) ** 9,10/3. Estadedip** - (ES ta DEE dip)

**10,5/2. Stardedip** - (star DEE dip) ** 10,8/3. Stodedip** - (sto DEE dip) ** 10,10/3. Distadedip** - (DISS ta DEE dip)

**P,N/M. P,N/M-Dip** - (pa NIM dip) - I guess these can be called the "panimdips"

**5/2,8/3. Stastodip** - (STAS toe dip) ** 5/2,10/3. Stastidedip** - (stast IDE dee dip) ** 8/3,10/3. Stostidedip** - (sto STIDE dee dip)

**N/M,P/Q. N/M,P/Q-Dip** - (NIM pik dip) - you guessed it, these are the "nimpiqdips"

Special thanks to Dr. Richard Klitzing for some of the heptagonal and enneagonal short names as well as helping me to keep these names from clashing with others.

**Conjugates**

The following are self-conjugate: triddip, thiddip, tisdip, shiddip, hiddip, and ostodip.

The following are conjugate pairs: odip-stodip, todip-tistodip, sodip-sistodip, and hodip-histodip.

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