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Temporary potpourri of incmats files, which still are to be shifted at a better place ...



Convex polyhedra with equal-sized edges but (some) non-regular faces   (up)

File Name Remarks
pacop pacop – partially contracted octagonal prism polyhedron with {(h,H,H)2} hexagons, h = 90°, H = 135°
mono-lower-sirco mono lowered small rhombicuboctahedron polyhedron with {(h,H,H)2} hexagons, h = 90°, H = 135°
para-bi-lower-tic para bi lowered truncated cube polyhedron with {(h,H,H)2} hexagons, h = 90°, H = 135°
mono-lower-tic mono lowered truncated cube polyhedron with {(h,H,H)2} hexagons, h = 90°, H = 135°
tet-lower-sirco patex sirco – partially tetrahedrally-expanded small rhombicuboctahedron,
tetrahedrally lowered small rhombicuboctahedron
polyhedron with {(h,H,H)2} hexagons, h = 90°, H = 135°
4fold-contr-tic pactic – partially contracted truncated cube polyhedron with {(h,H,H)2} hexagons, h = 90°, H = 135°
4fold-elong-co pexco – partially elongated cuboctahedron polyhedron with {(h,H,H)2} hexagons, h = 90°, H = 135°
4fold-elong-rhombohedron ebauco – elongated biaugmented cuboctahedron polyhedron with {(h,H,H)2} hexagons, h = 90°, H = 135°
and rhombs {(r,R)2}, r = 60°, R = 120°
pextoe pextoe – partially expanded truncated octahedron polyhedron with {(h,H,H)2} hexagons, h = 90°, H = 135°
pacgirco pac girco – partially contracted great rhomicuboctahedron polyhedron with {(h,H,H)2} hexagons, h = 90°, H = 135°
tet-trunc-cube patex cube – partially tetrahedrally-expanded cube,
tetrahedrally truncated cube, chamfered tetrahedron
polyhedron with {(h,H,H)2} hexagons, h = 90°, H = 135°
oct-trunc-rad octahedrally truncated rad, chamfered cube polyhedron with {(h,H,H)2} hexagons, h = 109.471221°, H = 125.264390°
cube-trunc-rad cubically truncated rad, chamfered oct polyhedron with {(h,H,H)2} hexagons, h = 70.528779°, H = 144.735610°.
ike-trunc-rhote icosahedrally truncated rhote, chamfered doe polyhedron with {(h,H,H)2} hexagons, h = 116.565051°, H = 121.717474°.
doe-trunc-rhote dodecahedrally truncated rhote, chamfered ike polyhedron with {(h,H,H)2} hexagons, h = 63.434949°, H = 148.282526°.
bauco bi-augmented cuboctahedron polyhedron with {(r,R)2} rhombs, r = 60°, R = 120°
t32s6h12 expanded octa-augmented truncated-octehedral variant polyhedron (T.Dorozinski) with {(H,h,h)2} hexagons, h = 109.47°, H = 141.06°
12aug-sirco dodeca-augmented rhombicuboctahedron polyhedron (T.Dorozinski) with {(h,H)3} hexagons, h = 104.48°, H = 135.52°
30aug-srid triaconta-augmented rhombicosidodecahedron polyhedron (Klitzing & Dorozinski) with {(h,H)3} hexagons, h = 115.28°, H = 124.72°
t12s12p12h8 octahedrally expanded icosidodecahedron polyhedron (T.Dorozinski) with {(h,H)3} hexagons, h = 82.24°, H = 157.76°
ex12aug-girco expanded dodeca-augmented great rhombicuboctahedron polyhedron (T.Dorozinski) with {(d,d,D,D)3} dodecagons, d = 142.24°, D = 157.76°
t8r24 rhombi-propello-octahedron relaxed polyhedron (J.McNeill) with rhombs (angles?)
t20r60 rhombi-propello-icosahedron relaxed polyhedron (J.McNeill) with rhombs (angles?)
t24s6r12 rhombical octa-augmented truncated-octehedral variant polyhedron (C.Piché) with rhombs, r = 38.94°, R = 141.06°
rhode (new: rad) rhombical dodecahedron (dual of co) polyhedron with rhombs, r = 70.53°, R = 109.47°
rhote (old: rattic) rhombical triacontahedron (dual of id) polyhedron with rhombs, r = 63.43°, R = 116.57°
r30+r60 rhombical enneacontahedron polyhedron with rhombs, r = 70.53°, R = 109.47° resp. r' = 41.81°, R' = 138.19°
t8s30r12 expanded rhombical dodecahedron polyhedron with rhombs, r = 70.53°, R = 109.47°
t20s60r30p12 expanded rhombical triacontahedron polyhedron with rhombs, r = 63.43°, R = 116.57°
s60r60p12h30 ... polyhedron (T.Dorozinski) with rhombs, r = 70.53°, R = 109.47°,
and (h,H,H)2 hexagons, h = 41.81°, H = 159.09°
p12h4 unit edge variant of truncation of tut dual polyhedron (T.Dorozinski) with {(P,p,P0,p,P)} pentagons and {(h,H)3} hexagons
xofo5ofox_xt pentagonal rhombic barrel, xofo5ofox&#xt,
stack of segments from id (polar) and doe (equatorial)
polyhedron (T.Dorozinski) with rhombs, r = 72°, R = 108°
phexdo partially hexa-expanded doe polyhedron (T.Dorozinski) with rhombs, r = 36.26°, R = 143.74°
phexik partially hexa-expanded ike polyhedron (T.Dorozinski) with {(h,H)3} hexagons, h = 97.76°, H = 142.24°

Convex polychora with equal-sized edges but (some) non-regular faces   (up)

File Name Remarks
trip=gybef trip || gybef polychoron either with corealmic cells or otherwise
using rhombs {(r,R)2}, r = 60°, R = 120°
abx3ooo3ooc4odo_zx chamfered hex polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°
and rhombs {(r,R)2}, r = 60°, R = 120°
abo3ooo3ooc4odo_zx terminally chamfered hex polychoron with rhombs {(r,R)2}, r = 60°, R = 120°
pexrit partially Stott expanded rit polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°
pabexrit partially Stott bi-expanded rit,
partially Stott bi-contracted tat
polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°
pactat partially Stott contracted tat polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°
pexrico partially Stott expanded rico polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°
pabexrico partially Stott bi-expanded rico,
partially Stott bi-contracted proh
polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°
pacproh partially Stott contracted proh polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°
pextah partially Stott expanded tah polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°
pabextah partially Stott bi-expanded tah,
partially Stott bi-contracted grit
polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°
pacgrit partially Stott contracted grit polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°
pextico partially Stott expanded tico polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°
pabextico partially Stott bi-expanded tico,
partially Stott bi-contracted gidpith
polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°
pac gidpith partially Stott contracted gidpith polychoron with {(h,H,H)2} hexagons, h = 90°, H = 135°

Honeycombs with equal-sized edges and convex cells but (some) non-regular faces   (up)

File Name Remarks
radh rhombic-dodecahedral honeycomb honeycomb with rhombs, r = 70.53°, R = 109.47°
extoh expanded octahedral-tetrahedral honeycomb honeycomb with rhombs, r = 70.53°, R = 109.47°
atich alternatedly truncated cubical honeycomb honeycomb with non-regular hexagons {(h,H,H)2}, h = 90°, H = 135°
octet-wise-trunc-radh alternated-cubically truncated rhombidodecahedral honeycomb honeycomb with non-regular hexagons {(h,H,H)2}, h = 109.471221°, H = 125.264390°
chon-wise-trunc-radh cubically truncated rhombidodecahedral honeycomb honeycomb with non-regular hexagons {(h,H,H)2}, h = 70.528779°, H = 144.735610°

Some non-self-intersecting, so concave polyhedra with regular faces (nsiCvRF)   (up)

File Name Remarks
xfo3foo5oxf_zx 20 doe-dimples + 12 id-dimples dihedral angle between {5a} and {5a}:   360°-arccos(-1/sqrt(5)) = 243.434949°
dihedral angle between {3} and {5b}:   360°-arccos(-sqrt[(5+2 sqrt(5))/15]) = 217.377°
xfo3foo5xuFx_zx 20 doe-dimples + 12 ti-dimples dihedral angle between {5a} and {5a}:   360°-arccos(-1/sqrt(5)) = 243.434949°
dihedral angle between {6} and {6}:   360°-arccos(-sqrt(5)/3) = 221.810315°
dihedral angle between {5b} and {6}:   360°-arccos(-sqrt[(5+2 sqrt(5))/15]) = 217.377368°

Some non-self-intersecting, so concave polychora with regular faces (nsiCvRF)   (up)

File Name Remarks
pautpen penta-augmented truncated pentachoron dihedral angle at {6} between tricu and tricu:   360°-arccos(-11/16) = 226.567463°
spysp small pyramidic swirlprism dihedral angle at {5} between peppy and peppy:   216°
hi-120ikadoes   hi dimpled in by 120 ikadoes dihedral angle at {3} between ike and tet:   360°-arccos[-sqrt(5/8)] = 217.761244°,
one type of those at {3} between tet and tet:   360°-arccos[-(1+3 sqrt(5))/8] = 195.522488°

Some non-self-intersecting, so concave polyhedra with (some) non-regular faces   (up)

File Name Remarks
xfoa3fooo5oxfo_zx 41st stellation of ti polyhedron with rhombs, r = 60°, R = 120°
(where a = sqrt(5) = 2.236068)

Some convex polyhedra with different edge sizes   (up)

File Name Remarks
m m3o co oo3ox&#zy, tridpy variant,
pen derived,
dual of trip
using edge sizes x and y = 2/3
cell of o3m3o3o
co2oo3ox_zy-o4m3o3o co oo3ox&#zy, tridpy variant,
tes derived
using edge sizes x and y = sqrt(7/18) = 0.623610
cell of o4m3o3o
co2oo3ox_zy-o5m3o3o co oo3ox&#zy, tridpy variant,
hi derived
using edge sizes x and y = sqrt[(9-sqrt(5))/18] = 0.613004
cell of o5m3o3o
co2oo3ox_zy-o3m4o3o co oo3ox&#zy, tridpy variant,
ico derived
using edge sizes x and y = sqrt(5)/3 = 0.745356
cell of o3m4o3o
oct qo oo4ox&#zx,
hex derived
using edge sizes x only (Wythoffian)
cell of o3m3o4o
co2oo5ox_zy-o3m3o5o co oo3ox&#zy, pedpy variant,
ex derived
using edge sizes x and y = sqrt[(6+2 sqrt(5))/5] = 1.447214
cell of o3m3o5o
oqo3coc_xt oqo3coc&#xt, truncated tridpy variant,
o2o3o symmetric co relative
using edge sizes x and c = 1/sqrt(2) = 0.707107,
relates to pen edges
obo3coc_xt-ico oqo3coc&#xt, truncated tridpy variant,
o2o3o symmetric co relative
using edge sizes x and c = b/2 = 1/sqrt(3) = 0.577350,
relates to ico edges
obo3coc_xt-tes oqo3coc&#xt, truncated tridpy variant,
o2o3o symmetric co relative
using edge sizes x and c = b/2 = sqrt(2/3) = 0.816497,
relates to tes edges
obo3coc_xt-hi oqo3coc&#xt, truncated tridpy variant,
o2o3o symmetric co relative
using edge sizes x and c = b/2 = sqrt[(5+sqrt(5))/10] = 0.850651,
relates to hi edges
co oqo4xox&#xt using edge sizes x only (Wythoffian),
relates to hex edges
oqo5coc_xt oqo5coc&#xt, truncated pedpy variant,
o2o5o symmetric co relative
using edge sizes x and c = (1+sqrt(5))/sqrt(8) = 1.144123,
relates to ex edges
vov3ofx_xt vov3ofx&#xt, axially trigonal variant of pentagonal rotunda using edge sizes x and v = (sqrt(5)-1)/2 = 0.618034
tet-dim-doe tetrahedrally-diminished dodecahedron using edge sizes x and f = (1+sqrt(5))/2 = 1.618034
cube-dim-doe oxF xFo Fox&#zf, cubically-diminished dodecahedron,
pyritohedrally symmetric variant of ike
using edge sizes x and f = (1+sqrt(5))/2 = 1.618034
oxqxo8ooooo&#qt octagonal Leonardo style "polyhedron of renaissance" using edge sizes x and q = sqrt(2) = 1.414214
24t6s8n xA3Bo4oC&#zx, near miss Johnson solid with enneagons using edge sizes x and C = 1.049668

Further polyhedra with different edge sizes occur naturally either within the investigation of Catalan solids or as cells of their 4D counterparts.


Some convex polychora with different edge sizes   (up)

File Name Remarks
o3m3o3o dual of rectified pentachoron,
polychoron co3oo3oo3ox&#zy
Catalan polychoron, using edge sizes x and y = 2/3
(pseudo edge size c = 2/3)
o4m3o3o dual of rectified tesseract,
polychoron co4oo3oo3ox&#zy
Catalan polychoron, using edge sizes x and y = sqrt(7/18) = 0.623610
(pseudo edge size c = sqrt(2)/3 = 0.471405)
o5m3o3o dual of rectified hecatonicosachoron,
polychoron co5oo3oo3ox&#zy
Catalan polychoron, using edge sizes x and y = sqrt[(9-sqrt(5))/18] = 0.613004
(pseudo edge size c = (sqrt(5)-1)/3 = 0.412023)
o3m4o3o dual of rectified icositetrachoron,
polychoron co3oo4oo3ox&#zy
Catalan polychoron, using edge sizes x and y = sqrt(5)/3 = 0.745356
(pseudo edge size c = sqrt(8)/3 = 0.942809
ico dual of rectified hexadecachoron = ico,
polychoron qo3oo3oo4ox&#zx
Catalan polychoron, using edge sizes x only
(Wythoffian)
o3m3o5o dual of rectified hexacosachoron,
polychoron co3oo3oo5ox&#zy
Catalan polychoron, using edge sizes x and y = sqrt[(6+2 sqrt(5))/5] = 1.447214
(pseudo edge size c = (5+3 sqrt(5))/5 = 2.341641
oq3oo3qo3oc_zx pentachoron-derived Gévay polychoron oq3oo3qo3oc&#zx perfect polychoron, using edge sizes x and c = 1/sqrt(2) = 0.707107
rico hexadecachoron-derived Gévay polychoron oq3oo3qo4ox&#zx perfect polychoron, using edge size x only (Wythoffian)
oq3oo3qo5oc_zx hexacosachoron-derived Gévay polychoron oq3oo3qo5oc&#zx perfect polychoron, using edge sizes x and c = (1+sqrt(5))/sqrt(8) = 1.144123
oa3oo4bo3oc_zx icositetrachoron-derived Gévay polychoron oa3oo4bo3oc&#zx perfect polychoron, using edge sizes x and c = 1/sqrt(3) = 0.577350
oa4oo3bo3oc_zx tesseract-derived Gévay polychoron oa4oo3bo3oc&#zx perfect polychoron, using edge sizes x and c = sqrt(2/3) = 0.816497
oa5oo3bo3oc_zx hecatonicosachoron-derived Gévay polychoron oa4oo3bo3oc&#zx perfect polychoron, using edge sizes x and c = sqrt[(5+sqrt(5))/10] = 0.850651
xuo3uoo3oou3oux_zqqh decachoron-derived Gévay polychoron xuo3uoo3oou3oux&#z(q,q,h) perfect polychoron, using edge sizes x, q = sqrt(2) = 1.414214, and h = sqrt(3) = 1.732051
aco3boo4oob3oca_zxxd tetracontoctachoron-derived Gévay polychoron aco3boo4oob3oca&#z(x,x,d) perfect polychoron, using edge sizes x, a = (sqrt(8)-1)/sqrt(3) = 1.055643, and d = sqrt[(6-sqrt(2))/3] = 1.236364
doe-rico rectified icositetrachoron-derived polychoron with dodecahedra using edge sizes x and v = (sqrt(5)-1)/2 = 0.618034

Further polychora with different edge sizes occur naturally within the investigation of the 4D counterparts of the Catalan solids.


Polyhedra of higher genus   (up)

File Name Remarks
4_5__19 {4,5;19}, i.e. combinatorically regular {4,5} of genus 19 polyhedral relization using rhombs of 2 sizes and trapezia
4_5__31 {4,5;31}, i.e. combinatorically regular {4,5} of genus 31 polyhedral relization using 4 types of trapezia and squares of 2 sizes
5_4__13 {5,4;13}, i.e. combinatorically regular {5,4} of genus 13 polyhedral relization using 4 types of pentagons



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