Category 13: Prismatorhombates and Kin


This category contains 14 regiments of three, 42 polytera total. Their verfs look like either trapezoid-dyad disphenoids or trapezoid pyramid pyramids (trapezoid scalenes) and their two facetings. We can split this category into three groups: the prismatorhombates (four regiments), the convex regiment kin (five regiments), and the star regiment kin (five regiments). The prismatorhombates are the oxxox cases, the two kin cases are xoxxx and xxoxx. All of these are tame.
Glaprin

Prismatorhombates

Prismatorhombate Verfs

There are four regiments of three. These are the oxxox cases and they have trapezoid disphenoid verfs along with their two facetings. Each regiment contains two orientable members and then the non-orientable one (the lepido member). The pirx regiment has hixic symmetry and has 180 vertices, the others have penteractic symmetry with 960 vertices. Pirx, prin, and pirt are convex. Above are the verfs as a series of cross sections.

830. Pirx - (PIRKS) prismatorhombated hexateron. Its symbol is oxxox. It has 6 prips, 6 decas, 15 tuttips, and 20 triddips.

831. Rapirx - (RAY pirks) retroprismatorhombated hexateron. Its symbol is ox(xo,x). It has 6 pittips, 6 decas, 6 grips, and 20 triddips.

832. Lapirx - (LAY pirks) lepidoprismatorhombated hexateron. It has 6 ripdips, 6 grips, and 15 tuttips.

833. Prin - (PRIN) prismatorhombated penteract. Its symbol is oxxo'x. It has 10 prits, 32 decas, 80 tuttips, and 80 tisdips.

834. Sibtadin - (SIB ta din) small biprismato32dispenteract. Its symbol is ox(x'x"o) = oxS (S for socco). It has 10 sichadoes, 32 decas, 10 grits, and 80 tisdips.

835. Slaprin - (SLAP rin) small lepidoprismatorhombated penteract. It has 10 sirpdoes, 10 grits, and 80 tuttips.

836. Pirt - (PIRT) prismatorhombated 32teron. Its symbol is xoxx'o = xo$x. It has 32 prips, 10 tahs, 40 topes, and 80 tisdips.

837. Repirt - (RE pirt) retroprismatorhombated 32teron. Its symbol is (x,ox)x'o = (x,o$)x. It has 32 pittips, 10 tahs, 10 ticoes, and 80 tisdips.

838. Lepirt - (LE pirt) lepidoprismatorhombated 32teron. It has 32 ripdips, 10 ticoes, and 40 topes.

839. Gibtadin - (GIB ta din) great biprismato32dispenteract. Its symbol is (o'x"x)xo = Gxo. It has 10 gichadoes, 10 gaqrits, 32 decas, and 80 tisdips.

840. Quiprin - (KWIP rin) quasiprismatorhombated penteract. Its symbol is oxxo"x. It has 10 paqrits, 32 decas, 80 tuttips, and 80 tisdips.

841. Glaprin - (GLAP rin) great lepidoprismatorhombated penteract. It has 10 girpdoes, 10 gaqrits, and 80 tuttips.

Below are fields of 3-D poke-sections of the prismatorhombates except for quiprin, I have yet to code in paqrit poke sections.

Pirx Regiment

Prin Regiment

Pirt Regiment

Gibtadin Regiment


Convex Regiment Kin of the Prismatorhombates

Convex Kin Verfs

Convex Kin Verfs

Kin to the prismatorhombates are the xoxxx and xxoxx cases. There are five convex and five star regiments, each having three members. The convex regiments are mentioned here. Cograx has hixic symmetry and captid has dotic symmetry, both have 360 vertices, while the other regiments have pentic symmetry with 1920 vertices. These all have trapezoid scalene verfs along with their facetings. Like the last group, each regiment has two orientable members and a non-orientable one (the lepido cases). Verfs are above in sections.

842. Cograx - (KO graks) celligreat rhombated hexateron. Its symbol is xoxxx. It has 6 prips, 15 copes, 6 grips, 15 topes, and 20 thiddips.

843. Rocgrax - (ROK graks) retrocelligreat rhombated hexateron. Its symbol is (x,ox)xx. It has 6 pittips, 15 ohopes, 6 grips, 6 gippids, and 20 thiddips.

844. Locgrax - (LOK graks) lepidocelligreat rhombated hexateron. It has 6 ripdips, 15 chopes, 6 gippids, and 15 topes.

845. Captid - (CAP tid) celliprismatotruncated dodecateron. Its symbol is xxoxx. It has 12 prips, 30 tuttips, and 20 hiddips.

846. Recaptid - (re CAP tid) retrocelliprismatotruncated dodecateron. Its symbol is x(x,ox)x. It has 12 pittips, 30 tuttips, and 6 gippids.

847. Lacaptid - (la CAP tid) lepidocelliprismatotruncated dodecateron. It has 12 ripdips, 6 gippids, and 20 hiddips.

848. Cogrin - (KO grin) celligreat rhombated penteract. Its symbol is xoxx'x. It has 10 grits, 32 prips, 40 gircopes, 80 copes, and 80 todips.

849. Srocgrin - (SROK grin) small retrocelligreat rhombated penteract. Its symbol is (x,ox)x'x. It has 10 grits, 32 pittips, 80 ohopes, 80 todips, and 10 gidpiths.

850. Slocgrin - (SLOK grin) small lepidocelligreat rhombated penteract. It has 32 ripdips, 40 gircopes, 80 chopes, and 10 gidpiths.

851. Cogart - (KO gart) celligreat rhombated 32teron. Its symbol is xxxo'x. It has 10 prits, 32 grips, 40 sircopes, 80 topes, and 80 shiddips.

852. Sibcotdin - (sib COT din) small biprismatocelli32dispenteract. Its symbol is xx(x'x"o) = xxS. It has 10 sichadoes, 10 gidpiths, 32 grips, 40 soccopes, and 80 shiddips.

853. Slocgart - (SLOK gart) small lepidocelligreat rhombated 32teron. It has 10 sirpdoes, 10 gidpiths, 40 srohps, and 80 topes.

854. Captint - (CAP tint) celliprismatotruncated penteracti32teron. Its symbol is xxox'x. It has 10 prohs, 32 prips, 40 ticcups, 80 tuttips, and 80 hodips.

855. Sircaptint - (sir CAP tint) small retrocelliprismatotruncated penteracti32teron. Its symbol is x(x,ox)'x. It has 10 siphadoes, 32 pittips, 40 ticcups, 80 tuttips, and 10 gidpiths.

856. Slacpotint - (SLAK po tint) small lepidocelliprismatotruncated penteracti32teron. It has 10 sirpiths, 32 ripdips, 80 hodips, and 10 gidpiths.

Below are fields of 3-D poke-section of each of the polytera in same order.

Cograx Regiment

Captid Regiment

Cogrin Regiment

Cogart Regiment

Captint Regiment


Star Regiment Kin of the Prismatorhombates

Star Kin Verfs

Star Kin Verfs

These are the five star regiments, each with three members. All of these have pentic symmetry with 1920 vertices. Their verfs are just like the last group, trapezoid scalenes. Also the third regiment member is non-orientable, while the other two are orientable. The verfs are above.

857. Quacgarn - (KWAK garn) great penteractipenteracti32teron. Its symbol is xoxx"x. It has 10 gaqrits, 32 prips, 40 quitcopes, 80 copes, and 80 tistodips.

858. Gorcgrin - (GORK grin) great retrocelligreat rhombated penteract. Its symbol is (x,ox)x"x. It has 10 gaqrits, 32 pittips, 80 ohopes, 80 tistodips, and 10 gaquidpoths.

859. Golcgrin - (GOLK grin) great lepidocelligreat rhombated penteract. It has 32 ripdips, 40 quitcopes, 80 chopes, and 10 gaquidpoths.

860. Quicpatint - (KWIK pa tint) quasicelliprismatotruncated penteracti32teron. Its symbol is xxox"x. It has 10 quiprohs, 32 prips, 40 quithips, 80 tuttips, and 80 histodips.

861. Gircaptint - (gir CAP tint) great retrocelliprismatotruncated penteracti32teron. Its symbol is x(x,ox)"x. It has 10 giphadoes, 32 pittips, 40 quithips, 80 tuttips, and 10 gaquidpoths.

862. Glacpotint - (GLAK po tint) great lepidocelliprismatotruncated penteracti32teron. It has 10 girpiths, 32 ripdips, 80 histodips, and 10 gaquidpoths.

863. Niptant - (NIP tant) penteractiprismatotruncated penteracti32teron. Its symbol is xo(x'x"x) = xoC. It has 10 thatoths, 10 prohs, 32 prips, 40 cotcopes, and 80 tistodips.

864. Narptint - (NARP tint) penteractiretroprismatotruncated penteracti32teron. Its symbol is (x,o(x)'x"x). It has 10 thatoths, 10 siphadoes, 32 pittips, 10 thatpaths, and 80 tistodips.

865. Nalpitant - (NAL pit ant) penteractilepidoprismatotruncated penteracti32teron. It has 10 sirpiths, 32 ripdips, 40 cotcopes, and 10 thatpaths.

866. Naquiptant - (na KWIP tant) penteractiquasiprismatotruncated penteracti32teron. Its symbol is (x'x"x)ox = Cox. It has 10 quiprohs, 10 thaquitoths, 32 prips, 40 cotcopes, and 80 todips.

867. Noqraptant - (no KRAP tant) penteractiquasiretroprismatotruncated penteracti32teron. Its symbol is (x'x"(x)o,x). It has 10 giphadoes, 10 thaquitoths, 32 pittips, 10 thaquitpaths, and 80 todips.

868. Naqleptint - (na KLEP tint) penteractiquasilepidoprismatotruncated penteracti32teron. It has 10 girpiths, 32 ripdips, 40 cotcopes, and 10 thaquitpaths.

869. Gibcotdin - (gib COT din) great biprismatocelli32dispenteract. Its symbol is Gxx = (o'x"x)xx. It has 10 gaquidpoths, 10 gichadoes, 32 grips, 40 goccopes, and 80 shiddips.

870. Quicgrat - (QUIK grat) quasicelligreat rhombated 32teron. Its symbol is xxxo"x. It has 10 paqrits, 32 grips, 40 quercopes, 80 topes, and 80 shiddips.

871. Glocgart - (GLOK gart) great lepidocelligreat rhombated 32teron. It has 10 gaquidpoths, 10 girpdoes, 40 grohps, and 80 topes.

Below are fields of 3-D poke-section of most of these (only quicgrat is missing, since I have yet to code in paqrit poke sections).

Quacgarn Regiment

Quicpatint Regiment

Niptant Regiment

Naquiptant Regiment

Gibcotdin Regiment


Conjugates

Below shows how the rectates pair up as conjugates.

Conjugates

The following are self conjugates: pirx, rapirx, lapirx, pirt, repirt, lepirt, cograx, rocgrax, locgrax, captid, recaptid, and lacaptid.

The following are conjugate pairs: prin-quiprin, sibtadin-gibtadin, slaprin-glaprin, cogrin-quacgarn, srocgrin-gorcgrin, slocgrin-golcgrin, cogart-quicgrat, sibcotdin-gibcotdin, slocgart-glocgart, captint-quicpatint, sircaptint-gircaptint, slacpotint-glacpotint, niptant-naquiptant, narptint-noqraptant, and nalpitant-naqleptint.

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