Category 10: Greater Truncates

There are 26 greater truncates, they include the great rhombates (ooxxx cases), great birhombates (oxxxo cases), great prismates (oxxxx cases) and the omnitruncates (xxxxx cases) along with those with similar verfs. All of these are tame and only grahehad is non-orientable. The gart regiment has two members, the others have one, I call one member regiments "lone operatives".

Great Rhombates

Great Rhombate Verfs

These seven have verfs shaped like regular polygon (or faceting) scalenes (aka polygon pyramid pyramids). All of them have pentic symmetry except for garx which has hixic symmetry. Garx has 120 vertices. Gart and grahehad which form a regiment has 480 vertices, the others have 640. The first three are convex. Above are the verfs as a series of cross sections.

723. Garx - (GARKS) great rhombated hexateron, also known as cantitruncated hexateron. Its symbol is ooxxx. It has 6 grips, 6 tips, and 15 tepes.

724. Girn - (GURN) great rhombated penteract, also known as cantitruncated penteract. Its symbol is ooxx'x. It has 10 grits, 32 tips, and 80 tepes.

725. Gart - (GART) great rhombated 32teron, also known as cantitruncated pentacross. Its symbol is xxxo'o = xx9o. It has 10 thexes, 32 grips, and 40 opes.

726. Grahehad - (GRAH he had) great rhombated hexadecahemidodecateron. It is a member of the gart regiment and is the only non-orientable polyteron in this category. It has 10 tithoes, 16 grips, 40 thahps, and 5 ticoes.

727. Gaqrin - (GAH krin) great quasirhombated penteract, could also be called cantistellatruncated penteract. Its symbol is ooxx"x. It has 10 gaqrits, 32 tips, and 80 tepes.

728. Nottant - (NOT tant) penteractitruncated penteracti32teron. Its symbol is oo(x'x"x), or ooC for short where C stands for cotco. It has 10 thatoths, 10 tats, and 32 tips.

729. Naquitant - (NAK kwit ant) penteractiquasitruncated penteracti32teron. Its symbol is (x'x"x)oo = Coo. It has 10 quitits, 10 thaquitoths, and 32 tips.

Below are fields of 3-D poke-sections of each of the great rhombates in same order.

Great Rhombate Sections

Great Birhombates

Great Birhombate Verfs

These four have verfs which are disphenoid pyramids. Gibrid has dottic symmetry, girhin has hinnic, and the other two have pentic. All of them are convex except for danbitot. Gibrid has 180 vertices, girhin has 480, the other two have 960. Above are the verfs as a series of cross sections.

730. Gibrid - (GIB brid) great birhombated dodecateron, also known as bicantitruncated hexateron. The symbol is oxxxo. It has 12 grips and 20 triddips.

731. Gibrant - (gib BRANT) great birhombated penteracti32teron, also known as bicantitruncated penteract. Its symbol is oxxx'o = ox$x. It has 10 ticoes, 32 grips, and 80 tisdips.

732. Danbitot - (DAN bit ot) dispenteractibitruncated 32teron. Its symbol is o(x'x"x)o = oCo. It has 10 thaquitoths, 10 thatoths, and 32 decas.

733. Girhin - (GIR hin) great rhombated demipenteract, also called cantitruncated demipenteract. Its symbol is ox9x. It has 10 tahs, 16 grips, and 16 decas.

Below are fields of 3-D poke-sections of each of the great birhombates in same order.

Great Birhombate Sections

Great Prismates

Great Prismate Verfs

These nine have bilateral pentachoron verfs. The first three and giphin are convex. Gippix and giphin have hixic and hinnic symmetry respectively, the others have pentic. Gippix has 360 vertices, giphin has 960, the others have 1920. Verfs are above in sections.

734. Gippix - (GIP pix) great prismated hexateron, also called runcicantitruncated hexateron. Its symbol is oxxxx. It has 6 gippids, 6 grips, 15 tuttips, and 20 thiddips.

735. Gippin - (GIP pin) great prismated penteract, also called runcicantitruncated penteract. Its symbol is oxxx'x. It has 10 gidpiths, 32 grips, 80 tuttips, and 80 todips.

736. Gippit - (GIP pit) great prismated 32teron, also called runcicantitruncated pentacross. Its symbol is xxxx'o = xx$x. It has 10 ticoes, 32 gippids, 40 topes, and 80 shiddips.

737. Gaquapan - (GAH kwa pan) great quasiprismated penteract. Its symbol is oxxx"x. It has 10 gaquidpoths, 32 grips, 80 tuttips, and 80 tistodips.

738. Nurrant - (NUR rant) penteractirhombated penteracti32teron. Its symbol is ox(x'x"x) = oxC. It has 10 thatpaths, 10 grits, 32 grips, and 80 tistodips.

739. Sadinnert - (sa DIN nert) small dispenteractirhombated 32teron. Its symbol is o(x'x"x)x = oCx. It has 10 thaquitpaths, 10 thatoths, 32 grips, and 40 ticcups.

740. Gadinnert - (ga DIN nert) great dispenteractirhombated 32teron. Its symbol is x(x'x"x)o = xCo. It has 10 thaquitoths, 10 thatpaths, 32 grips, and 40 quithips.

741. Noqrant - (NO krant) penteractiquasirhombated penteracti32teron. Its symbol is (x'x"x)xo = Cxo. It has 10 gaqrits, 10 thaquitpaths, 32 grips, and 80 todips.

742. Giphin - (GIF fin) great prismated demipenteract. Its symbol is xx9x. It has 10 tahs, 16 gippids, 16 grips, and 40 tuttips.

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

Great Prismate Sections


Omnitruncate Verfs

These six have irregular pentachoron verfs. Gocad has dottic symmetry, the others have pentic. Gocad and gacnet are convex, the others are starry. Gocad has 720 vertices, the others have 3840. The verfs are above.

743. Gocad - (GO kad) great cellated dodecateron, also called omnitruncated hexateron. Its symbol is xxxxx. It has 12 gippids, 30 topes, and 20 hiddips.

744. Gacnet - (GAK net) great cellated penteracti32teron, also called omnitruncated penteract. Its symbol is xxxx'x. It has 10 gidpiths, 32 gippids, 40 gircopes, 80 topes, and 80 hodips.

745. Gaquacint - (GAH kwa sint) great quasicellated penteracti32teron. Its symbol is xxxx"x. It has 10 gaquidpoths, 32 gippids, 40 quitcopes, 80 topes, and 80 histodips.

746. Nippant - (NIP pant) penteractiprismated penteracti32teron. Its symbol is xx(x'x"x) = xxC. It has 10 thatpaths, 10 gidpiths, 32 gippids, 40 cotcopes, and 80 histodips.

747. Danpit - (DAN pit) dispenteractiprismated 32teron. Its symbol is x(x'x"x)x = xCx. It has 10 thaquitpaths, 10 thatpaths, 32 gippids, 40 quitcopes, and 40 gircopes.

748. Noquapant - (NOK kwa pant) penteractiquasiprismated penteracti32teron. Its symbol is (x'x"x)xx = Cxx. It has 10 gaquidpoths, 10 thaquitpaths, 32 gippids, 40 cotcopes, and 80 hodips.

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

Omnitruncate Sections


Below shows how the rectates pair up as conjugates.


The following are self conjugates: garx, gart, grahehad, gibrid, gibrant, danbitot, girhin, gippix, gippit, giphin, gocad, and danpit.

The following are conjugate pairs: girn-gaqrin, nottant-noquitant, gippin-gaquapan, nurrant-noqrant, sadinnert-gadinnert, gacnet-gaquacint, and nippant-noquapant.

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