Category 19: Prisms

These are the prisms of the 75 uniform polyhedra excluding the cube (which will form the tesseract) - giving us 74 members in this category.

Prisms of the Regulars

These are the prisms of the regular polyhedra and their regiment members, there are nine of these, the first four are convex, the last one thahp (a prism of a semiregular) was added to group it with ope. These polychora are related to the truncates, due to their verfs.

Tepe Gipe

889. Tepe - (TEEP) tetrahedron (tet) prism. Its cells are 2 tets and 4 trips. It's verf is a trigon pyramid. It has 8 vertices and has tepe symmetry. Symbol = oox x. It has 6 pieces with two types.

890. Ope - (OPE) octahedron (oct) prism. Its cells are 2 octs and 8 trips. It's verf is a square pyramid. It has 12 vertices and has ope symmetry. Symbol = xo'o x = oxo x. It has 10 pieces in two types. It forms a two member regiment with thahp.

891. Dope - (DOPE) dodecahedron (doe) prism. Its cells are 2 does and 12 pips. Its verf is a trigon pyramid. It has 40 vertices and has ipe symmetry. Symbol = oo^x x. It has 14 pieces in two types.

892. Ipe - (IPE) icosahedron (ike) prism. Its cells are 2 ikes and 20 trips. Its verf is a pentagonal pyramid. It has 24 vertices and has ipe symmetry. Symbol = xo^o x = sss x. It has 22 pieces in two types. It and gaddip form a regiment.

893. Gaddip - (GAD dip) great dodecahedron (gad) prism. It has 2 gads and 12 pips. Its verf is a star pyramid. It has 24 vertices and has ipe symmetry. Symbol = o*o^x x. It has 62 pieces with two types.

894. Sissiddip - (SIS sid dip) small stellated dodecahedron (sissid) prism. It has 2 sissids and 12 stips. Its verf is a pentagonal pyramid. It has 24 vertices and has ipe symmetry. Symbol = x*o^o x. It has 62 pieces with two types. It and gipe form a regiment.

895. Gipe - (GIPE) great icosahedron (gike) prism. The cells are 2 gikes and 20 trips. Its verf is a star pyramid. It has 24 vertices and has ipe symmetry. Symbol = o*ox x. It has 182 pieces in three types.

896. Gissiddip - (GIS sid dip) great stellated dodecahedron (gissid) prism. It has 2 gissids and 12 stips. Its verf is a trigon pyramid. It has 40 vertices and has ipe symmetry. Symbol = x*oo x. It has 62 pieces in two types.

897. Thahp - (THAWP) tetrahemihexahedron (thah) prism. The cells are 2 thahs, 4 trips, and 3 cubes. Its verf is a bowtie pyramid. It has 12 vertices and has tepe symmetry. It has 24 pieces with three types. It is in the ope regiment.

Prisms of the Truncates

These are the prisms of the truncates and quasitruncates, there are ten of these, the first five are convex. These polychora are related to the great rhombates, due to their verfs which are scalenoids.

Ticcup Quithip

898. Tuttip - (TUT tip) truncated tetrahedron (tut) prism. Its cells are 2 tuts, 4 trips, and 4 hips. It has 24 vertices and has tepe symmetry. Symbol = oxx x. It has 10 pieces with three types.

899. Ticcup - (TIC cup) truncated cube (tic) prism. Its cells are 2 tics, 6 ops, and 8 trips. It has 48 vertices and has ope symmetry. Symbol = ox'x x. It has 16 pieces in three types.

900. Tope - (TOPE) truncated octahedron (toe) prism. Its cells are 2 toes, 6 cubes, and 8 hips. It has 48 vertices and has ope symmetry. Symbol = xx'o x = xxx x. It has 16 pieces with three types.

901. Tiddip - (TID dip) truncated dodecahedron (tid) prism. Its cells are 2 tids, 12 dips, and 20 trips. It has 120 vertices and has ipe symmetry. Symbol = ox^x x. It has 34 pieces with three types.

902. Tipe - (TIPE) truncated icosahedron (ti) prism. Its cells are 2 tis, 12 pips, and 20 hips. It has 120 vertices and has ipe symmetry. Symbol = xx^o x. It has 34 pieces with three types.

903. Tigiddip - (tih JID dip) truncated great dodecahedron (tigid) prism. Its cells are 2 tigids, 12 dips, and 12 stips. It has 120 vertices and has ipe symmetry. Symbol = o*x^x x. It has 74 pieces in three types.

904. Tiggipe - (tig GIPE) truncated great icosahedron (tiggy) prism. Its cells are 2 tiggies, 12 stips, and 20 hips. It has 120 vertices and has ipe symmetry. Symbol = o*xx x. It has 194 pieces in four types.

905. Quithip - (QUITH thip) quasitruncated hexahedron (quith) prism. Its cells are 2 quiths, 6 stops, and 8 trips. It has 48 vertices and has ope symmetry. Symbol = ox"x x. It has 56 pieces with four types.

906. Quit Sissiddip - (quit SIS sid dip) quasitruncated small stellated dodecahedron (quit sissid) prism. Its cells are 2 quit sissids, 12 stiddips, and 12 pips. It has 120 vertices and has ipe symmetry. Symbol = o^x*'x x. It has 110 pieces with four types.

907. Quit Gissiddip - (quit GIS sid dip) quasitruncated great stellated dodecahedron (quit gissid) prism. Its cells are 2 quit gissids, 12 stiddips, and 20 trips. It has 120 vertices and has ipe symmetry. Symbol = ox*'x x. It has 122 pieces in three types.

Prisms of the Rectates

These are the prisms of the rectates and their regiments. There are four regiments of three, giving us 12 of these. Cope and iddip are convex. Their verfs are pyramids of rectangles (for the colonels) or bowties (other two regiment members).

Ohope Giddip

Cope regiment - has 24 vertices and has ope symmetry.

908. Cope - (COPE) cuboctahedron (co) prism. Its cells are 2 coes, 6 cubes, and 8 trips. Symbol = ox'o x = xox x. It has 16 pieces in three types.

909. Ohope - (O hope) octahemioctahedron (oho) prism. Its cells are 2 ohoes, 8 trips, and 4 hips. It has 48 pieces with three types.

910. Chope - (CHOPE) cubihemioctahedron (cho) prism. Its cells are 2 choes, 6 cubes, and 4 hips. It has 42 pieces with three types.

Iddip regiment - has 60 vertices and has ipe symmetry.

911. Iddip - (ID dip) icosidodecahedron (id) prism. Its cells are 2 ids, 12 pips, and 20 trips. Symbol = ox^o x. It has 34 pieces with three types.

912. Sidhiddip - (sid HID dip) small dodecahemidodecahedron (sidhid) prism. Its cells are 2 sidhids, 12 pips, and 6 dips. It has 96 pieces in three types. This is the only known polychoron with sidhids for cells.

913. Seihiddip - (si HID dip) small icosihemidodecahedron (seihid) prism. Its cells are 2 seihids, 20 trips, and 6 dips. It has 120 pieces in three types. This is the only known polychoron with seihids for cells.

Diddip regiment - has 60 vertices and has ipe symmetry.

914. Diddip - (DID dip) dodecadodecahedron (did) prism. Its cells are 2 dids, 12 stips, and 12 pips. Symbol = o*x^o x. It has 74 pieces in three types.

915. Sidhipe - (SID hipe) small dodecahemiicosahedron (sidhei) prism. It has 2 sidheis, 12 stips, and 10 hips. It has 156 pieces with three types. This is the only known polychoron with sidheis.

916. Gidhipe - (GID hipe) great dodecahemiicosahedron (gidhei) prism. It has 2 gidheis, 12 pips, and 10 hips. It has 314 pieces with six types. This is the only known polychoron with gidheis.

Giddip regiment - has 60 vertices and has ipe symmetry.

917. Giddip - (GID dip) great icosidodecahedron (gid) prism. The cells are 2 gids, 12 stips, and 20 trips. Symbol = ox*o x. It has 134 pieces in four types.

918. Gidhiddip - (gid HID dip) great dodecahemidodecahedron (gidhid) prism. It has 2 gidhids, 12 stips, and 6 stiddips. It has 134 pieces in four types. This is the only known polychoron with gidhids.

919. Geihiddip - (gi HID dip) great icosihemidodecahedron (geihid) prism. It has 2 geihids, 20 trips, and 6 stiddips. It has 182 pieces in four types. This is the only known polychoron with geihids.

Prisms of the Ditrigonaries

These are the prisms of the sidtid regiment. There are 3 of these. Sidtiddip's verf is a ditrigon pyramid, ditdiddip's is a propeller pyramid, while gidtiddip's is a tripod pyramid. These have 40 vertices and have ipe symmetry.

920. Sidtiddip - (SID tid dip) small ditrigonary icosidodecahedron (sidtid) prism. The cells are 2 sidtids, 12 stips, and 20 trips. Symbol = (o*xo) x. It has 74 pieces with three types.

921. Ditdiddip - (DIT did dip) ditrigonary dodecadodecahedron (ditdid) prism. Its cells are 2 ditdids, 12 stips, and 12 pips. Symbol = (o*'x^o) x. It has 218 pieces with five types.

922. Gidtiddip - (GID tid dip) great ditrigonary icosidodecahedron (gidtid) prism. Its cells are 2 gidtids, 12 pips, and 20 trips. Symbol = (ox^o,) x. It has 302 pieces in five types.

Prisms of the Rhombates

These are the prisms of the rhombates and their regiments. There are seven regiments of three, giving us 21 of these. Sircope and sriddip are convex. Their verfs are pyramids of trapezoids (for the colonels), cross-trapezoids (second member of regiment), or butterflies (third member). These are similar to the prismatorhombates due to their verfs.

Sriddip Quercope

Sircope regiment - has 48 vertices and has ope symmetry.

923. Sircope - (SIR cope) small rhombicuboctahedron (sirco) prism. The cells are 2 sircoes, 6+12 cubes, and 8 trips. Symbol = xo'x x. It has 28 pieces with four types.

924. Soccope - (SOC cope) small cubicuboctahedron (socco) prism. Its cells are 2 soccoes, 6 cubes, 6 ops, and 8 trips. Symbol = (x'x"o) x. It has 80 pieces with six types.

925. Srohp - (SROPE) small rhombihexahedron (sroh) prism. Its cells are 2 srohs, 12 cubes, and 6 ops. It has 92 pieces in six types.

Sriddip regiment - has 120 vertices and has ipe symmetry.

926. Sriddip - (SRID dip) small rhombicosidodecahedron (srid) prism. Its cells are 2 srids, 12 pips, 20 trips, and 30 cubes. Symbol = xo^x x. It has 64 pieces with four types.

927. Saddiddip - (suh DID dip) small dodekicosidodecahedron (saddid) prism. Its cells are 2 saddids, 12 pips, 20 trips, and 12 dips. Symbol = (o^'x^x) x. It has 194 pieces with six types.

928. Sirdip - (SIR dip) small rhombidodecahedron (sird) prism. Its cells are 2 sirds, 30 cubes, and 12 dips. It has 224 pieces with six types.

Radedip regiment - has 120 vertices and has ipe symmetry.

929. Radiddip - (ray DID dip) rhombidodecadodecahedron (raded) prism. Its cells are 2 radeds, 12 stips, 12 pips, and 30 cubes. Symbol = x*o^x x. It has 314 pieces in six types.

930. Ididdip - (i DID dip) icosidodecadodecahedron (ided) prism. Its cells are 2 ideds, 12 stips, 12 pips, and 20 hips. Symbol = (x*'o^x) x. It has 434 pieces in seven types.

931. Ripe - (RIPE) rhombicosahedron (ri) prism. Its cells are 2 ris, 30 cubes, 20 hips. It has 744 pieces with 12 types.

Goccope regiment - has 48 vertices and has ope symmetry.

932. Goccope - (GOC cope) great cubicuboctahedron (gocco) prism. Its cells are 2 goccoes, 6 stops, 6 cubes, and 8 trips. Symbol = (o'x"x) x. It has 64 pieces with five types.

933. Quercope - (QUER cope) quasirhombicuboctahedron (querco) prism. Its cells are 2 quercoes, 6+12 cubes, and 8 trips. Symbol = xo"x x. It has 490 pieces in 15 types.

934. Grohp - (GROPE) great rhombihexahedron (groh) prism. Its cells are 2 grohs, 6 stops, and 12 cubes. It has 200 pieces in eight types.

Gidditdiddip regiment - has 120 vertices and has ipe symmetry.

935. Gidditdiddip - (GID dit DID dip - say its name enough times and you'll sound like a frog) great ditrigonary dodekicosidodecahedron (gidditdid) prism. Its cells are 2 gidditdids, 12 stiddips, 12 pips, and 20 trips. Symbol = (o^x*'x) x. It has 154 pieces with five types.

936. Giidip - (GIDE dip) great icosicosidodecahedron (giid) prism. Its cells are 2 giids, 12 pips, 20 trips, and 20 hips. Symbol = (xo^'x) x. It has 1234 pieces in 16 types.

937. Giddipe - (gid DIPE) great dodekicosahedron (giddy) prism. Its cells are 2 giddies, 20 hips, and 12 stiddips. It has 518 pieces in eight types.

Gaddiddip regiment - has 120 vertices and has ipe symmetry.

938. Gaddiddip - (gah DID dip) great dodekicosidodecahedron (gaddid) prism. Its cells are 2 gaddids, 12 stips, 12 stiddips, and 20 trips. Symbol = (o*x*'x) x. It has 182 pieces with four types.

939. Qriddip - (KRID dip) quasirhombicosidodecahedron (qrid) prism. Its cells are 2 qrids, 12 stips, 20 trips, and 30 cubes. Symbol = xo*'x x. It has 982 pieces in 12 types.

940. Girdip - (GIRD dip) great rhombidodecahedron (gird) prism. Its cells are 2 girds, 12 stiddips, and 30 cubes. It has 1036 pieces in 14 types.

Siidip regiment - has 120 vertices and has ipe symmetry.

941. Siidip - (SIDE dip) small icosicosidodecahedron (siid) prism. Its cells are 2 siids, 12 stips, 20 trips, and 20 hips. Symbol = (xo*x) x. It has 94 pieces with four types.

942. Sidditdiddip - (SID dit DID dip) small ditrigonary dodekicosidodecahedron (sidditdid) prism. Its cells are 2 sidditdids, 12 stips, 20 trips, and 12 dips. Symbol = (x^x*'o) x. It has 238 pieces in six types.

943. Siddipe - (sid DIPE) small dodekicosahedron (siddy) prism. Its cells are 2 siddies, 20 hips, and 12 dips. It has 504 pieces in ten types.

Prisms of the Great Rhombates

These are the prisms of the great rhombates. There are seven of three. Gircope and griddip are convex. Their verfs are irregular tetrahedra. These are similar to the maximized polychora due to their verfs. Gircope, quitcope, and cotcope have ope symmetry, others have ipe symmetry.

Griddip Quitcope

944. Gircope - (GIR cope) great rhombicuboctahedron (girco) prism. The cells are 2 gircoes, 6 ops, 12 cubes, and 8 hips. Symbol = xx'x x. It has 28 pieces with four types.

945. Griddip - (GRID dip) great rhombicosidodecahedron (grid) prism. Its cells are 2 grids, 30 cubes, 12 dips, and 20 hips. Symbol = xx^x x. It has 64 pieces with four types. This is the flattest uniform polychoron.

946. Quitcope - (QUIT cope) quasitruncated cuboctahedron (quitco) prism. Its cells are 2 quitcoes, 12 cubes, 20 hips, and 6 stops. Symbol = xx"x x. It has 150 pieces in eight types.

947. Quitdiddip - (quit DID dip) quasitruncated dodecadodecahedron (quitdid) prism. Its cells are 2 quitdids, 12 stiddips, 12 dips, and 30 cubes. Symbol = x^x*'x x. It has 406 pieces with eight types.

948. Gaquatiddip - (GAH kwa TID dip) great quasitruncated icosidodecahedron (gaquatid) prism. Its cells are 2 gaquatids, 12 stiddips, 20 hips, and 30 cubes. Symbol = xx*'x x. It has 1142 pieces with 13 types.

949. Cotcope - (KOT cope) cuboctatruncated cuboctahedron (cotco) prism. Its cells are 2 cotcoes, 6 stops, 6 ops, and 8 hips. Symbol = (x'x"x) x. It has 64 pieces with five types.

950. Idtiddip - (id TID dip) icosidodecatruncated icosidodecahedron (idtid) prism. Its cells are 2 idtids, 12 stiddips, 12 dips, and 20 hips. Symbol = (x^x*'x) x. It has 154 pieces with five types.

Prisms of the Snubs

These are the prisms of the snubs. There are twelve of three. Snic and Sniccup are convex. Their verfs are pyramids of the verfs of the original snubs. Sniccup has ope symmetry, others have ipe symmetry. With the exceptions of seside and sirsid, these prisms are the only known uniform polychora with their snubs for cells.

Sniccup

951. Sniccup - (SNIK kup) snub cube (snic) prism. The cells are 2 snics, 6 cubes, and 8+24 trips. Symbol = ss's x. It has 40 pieces with four types.

952. Sniddip - (SNID dip) snub dodecahedron (snid) prism. Its cells are 2 snids, 12 pips, and 20+60 trips. Symbol = ss^s x. It has 94 pieces with four types.

953. Siddiddip - (sid DID dip) snub dodecadodecahedron (siddid) prism. Its cells are 2 siddids, 12 stips, 12 pips, and 60 trips. Symbol = s^s*s x. It has 434 pieces in eight types.

954. Gosiddip - (go SID dip) great snub icosidodecahedron (gosid) prism. Its cells are 2 gosids, 12 stips, and 20+60 trips. Symbol = ss*s x. It has 302 pieces with six types.

955. Sesidip - (see SIDE dip) small snub icosicosidodecahedron (seside) prism. Its cells are 2 sesides, 12 stips, 40 trips (as 20 pairs), and 60 trips. Symbol = (ss*s) x. It has 214 pieces with five types.

956. Isdiddip - (iss DID dip) inverted snub dodecadodecahedron (isdid) prism. Its cells are 2 isdids, 12 stips, 12 pips, and 60 trips. Symbol = s^s*'s x. It has 374 pieces with eight types.

957. Gisiddip - (gi SID dip) great inverted snub icosidodecahedron (gisid) prism. Its cells are 2 gisids, 12 stips, and 20+60 trips. Symbol = ss*'s x. It has 782 pieces with 14 types.

958. Sididdip - (side DID dip) snub icosidodecadodecahedron (sided) prism. Its cells are 2 sideds, 12 stips, 12 pips, and 20+60 trips. Symbol = (s^s*'s) x. It has 478 pieces in 11 types.

959. Gisdiddip - (giss DID dip) great snub dodekicosidodecahedron (gisdid) prism. Its cells are 2 gisdids, 24 stips (12 pairs), and 20+60 trips. Symbol = (s*s*'s) x. It has 602 pieces with 11 types.

960. Girsiddip - (gir SID dip) great (inverted) retrosnub icosidodecahedron (girsid) prism. Its cells are 2 girsids, 12 stips, and 20+60 trips. Symbol = s,s*'s x. It has 1802 pieces with 31 types.

961. Sirsiddip - (sir SID dip) small inverted retrosnub icosicosidodecahedron (sirsid) prism. Its cells are 2 sirsids, 12 stips, 40 trips (paired), and 60 trips. Symbol = (s,s*'s) x. It has 3062 pieces with 29 types.

962. Gidriddip - (gid JRID dip) great dirhombicosidodecahedron (gidrid) prism. Its cells are 2 gidrids, 24 stips (paired), 40 trips (paired), and 60 cubes (paired hemi). Symbol = [s*s,s*'s] x. It has 1282 pieces with 14 types.

Conjugates

Below shows how the prisms pair up as conjugates.

Conjugates

The following are self-conjugate: tepe, ope, thahp, tuttip, tope, cope, ohope, chope, diddip, ditdiddip, radiddip, ididdip, ripe, quitdiddip, cotcope, idtiddip, sniccup, sidedip, gisdiddip, and gidriddip.

The following are conjugate pairs: dope-gissiddip, ipe-gipe, gaddip-sissiddip, ticcup-quithip, tiddip-quit gissiddip, tipe-tiggipe, tigiddip-quit sissiddip, iddip-giddip, sidhiddip-gidhiddip, seihiddip-geihiddip, sidhipe-gidhipe, sidtiddip-gidtiddip, sircope-quercope, soccope-goccope, srohp-grohp, sriddip-qriddip, saddiddip-gaddiddip, sirdip-girdip, siidip-giidip, sidditdiddip-gidditdiddip, siddipe-giddipe, gircope-quitcope, griddip-gaquatiddip, sniddip-gisiddip, and siddiddip-isdiddip.

The following are semi-conjugates: sesidip-sirsiddip, and gosiddip-girsiddip.

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