### Segmentotopes

In 2000 Klitzing published on segmentotopes in general resp. his research on convex segmentochora in special. Segmentotopes are polytopes which bow to the following conditions:

• all vertices on the surface of 1 hypersphere
• all vertices on 2 parallel hyperplanes
• all edges of 1 length

The first condition shows that the circumradius is well defined. Moreover, in union with condition 3 this implies that all 2D faces have to be regular. The sandwich type 2nd condition implies that all edges, which aren't contained completely within one of the hyperplanes, would join both, i.e. having one vertex each in either plane. Thence segmentotopes have to be monostratic. In fact, segmentotopes are the monostratic orbiforms. (Orbiforms, a terminus which had been created several years later only, just use the first and third condition of those.) Finally it follows, that the bases have to be orbiforms, while all the lacing elements have to be (lower dimensional) segmentotpes.

The naming of individual segmentotopes usually is based on the 2 base polytopes: top-base polytope atop bottom-base polytope. Symbolically one uses the parallelness of those bases: Ptop || Pbottom. (For the smaller segmentotopes the choice of bases need not be unique.)

Segmentotopes are closely related to lace prisms. In fact those concepts have a large common intersection, but they are not identical. While lace prisms need an axis of symmetry (in fact one which is describable as Dynkin symbol), one uses the terminus "axis" in the context of segmentotopes only in the sense of the line defined by the centers of the circumspheres of d-1 dimensional bases. (Thus the topic of axial polytopes does more relate to lace towers (as multistratic generalizations of lace prisms) than to segmetotopes. None the less there is a large overlap.) – Note that the radius R of the d-1 dimensional circumsphere used for a segmentotpal base of dimension d-k might well be larger than the radius r of its d-k dimensional circumsphere: for k > 1 the latter might well be placed within the former with some additional shift s:   R2 = r2 + s2. For a simple example just consider squippy, the 4-fold pyramid, which is just half of an oct, when being considered as line || triangle: the subdimensional base, the single edge, there is placed off-set.

In fact, let rk be the individual circumradii of the bases, let sk be the respective shifts away from the axis (if subdimensional), let h be the axial height and R the global circumradius, then we have the following interrelation formula between all these sizes  4 R2 h2 = ((r22+s22)-(r12+s12))2 + 2 ((r12+s12)+(r22+s22)) h2 + h4.

### Convex Segmentochora   (up)

Just as polytopes are distinguished dimensionally as polygons, polyhedra, polychora, etc. so too are segmentotopes.
The only segmentogons (without any further adjectivic restriction) clearly are

• regular triangle   (point || line) and
• square   (line || line).

Segmentohedra already include infinite series like

(*) Grünbaumian bottom base understood to be withdrawn.
For convex ones d clearly has to be 1 and several of the above series then become finite.

Polychora generally have the disadvantage not being visually accessible. Segmentochora are not so hard for that: Just consider the 2 base polyhedra displayed concentrically, perhaps slightly scaled, while the lacings then get slightly deformed. Mathematically speaking, axial projections (view-point at infinity) and central projections (finite view-point), either one being taken on the axis for sure, from 4D onto 3D generally are well "viewable" for such monostratic figures. Especially when using real 3D graphics (like the here used VRMLs) instead of further projections onto 2D as in usual pictures: Note that all pictures at "segmentochoron display" within individual polychoron files will be linked to such VRML files.

 fore color back color explanation red - Ptop blue - Pbottom gold - lacing edges - white spherical geometry - light yellow euclidean geometry – cf. also: decompositions - light green hyperbolic geometry
##### Cases with Tetrahedral Axis: ##### Cases with Octahedral Axis: ##### Cases with Icosahedral Axis: ##### Cases with n-Prismatic or n-Antiprismatic Axis:
ortho n-gon n-prism gyrated n-prism 2n-prism n-antiprism
pt || n-p
(prism pyramids)
pt || n-ap
(antiprism pyramids)
point
line || ortho n-gon
(scalenes)
line || n-p
(pyramid prisms)
line segment
n-g || n-p
(3,n-duoprisms)
n-g || gyro n-p
(antifastegia)
n-g || 2n-p
(magnabicupolic rings,
pucofastegia)
n-g || n-ap
(= n-g || gyro n-p)
n-gon
2n-g || n-p
(orthobicupolic rings,
cupofastegia)
2n-g || n-ap
(gyrobicupolic rings)
2n-gon
n-p || n-p
(4,n-duoprisms)
n-p || gyro n-p
(antiprism prisms)
n-p || 2n-p
(n-cupola prisms)
n-prism
2n-p || 2n-p
(4,2n-duoprisms)
2n-prism
n-ap || n-ap
(= n-p || gyro n-p)
n-antiprism

##### Non-Lace-Prismatics:

Just as already often was used within the set of Johnson solids, several of the above segmentochora allow diminishings too. Those generally break some symmetries of one or both bases, and therefore too of the axial symmetry. Thus there is no longer a unifying symmetry according to which a Dynkin symbol could be designed, being the premise for lace prisms. Even though, such diminished ones are fully valid segmentotopes (following the above 3 conditions). An easy 3D example could be again line || triangle, the alternate description of the above mentioned squippy. The easiest 4D one clearly is squasc (i.e. the 1/4-lune of the hex). – Gyrations in some spare cases might apply as well, although those in general would conflict to the requirement of exactly 2 vertex layers.

But there is also a generic non-lace-prismatic convex segmentochoron with octahedral symmetry at one base, with icosahedral symmetry at the other. (The common subsymmetry clearly is the pyrital. But that one does not bow to Dynkin symbol description.) That one uses as faces 1 cube (as bottom base), 6 trip (as line || square), 12 squippy (as triangle || line), 8 tet (as triangle || point), and 1 ike (as top base). ##### Full Table:
0.632456
```K-4.1   pen = pt || tet        (regular)
K-4.1.1 pen = line || perp {3} (regular)
```
0.707107
```K-4.2   hex = tet || dual tet     (regular)

K-4.3   octpy = pt || oct         (segment of hex)
K-4.3.1 octpy = {3} || gyro tet   (segment of hex)

K-4.4   squasc = pt || squippy    (luna of hex)
K-4.4.1 squasc = line || tet      (luna of hex)
K-4.4.2 squasc = {3} || incl {3}  (luna of hex)
K-4.4.3 squasc = line || perp {4} (luna of hex)
```
0.774597
```K-4.5   rap = tet || oct            (uniform)

K-4.6   traf = tet || squippy       (segment of rap)
K-4.6.1 traf = {3} || oct           (segment of rap)
K-4.6.2 traf = {3} || gyro trip     (segment of rap)

K-4.7   trippy = line || squippy    (segment of rap)
K-4.7.1 trippy = {3} || tet         (segment of rap)
K-4.7.2 trippy = pt || trip         (segment of rap)
K-4.7.3 trippy = {3} || otho {4}    (segment of rap)
(where 1 {3}-edge || 2 {4}-edges)

K-4.8   bidrap = {3} || squippy     (wedge of rap)
K-4.8.1 bidrap = {4} || tet         (wedge of rap)
K-4.8.2 bidrap = line || ortho trip (wedge of rap)
```
0.790569
```K-4.9   tepe = tet || tet        (uniform)
K-4.9.1 tepe = line || para trip (uniform)
K-4.9.2 tepe = {4} || ortho {4}  (uniform)
```
0.816497
```K-4.10   triddip = {3} || trip         (uniform)

K-4.11   ope = oct || oct              (uniform)
K-4.11.1 ope = trip || gyro trip       (uniform)

K-4.12   squippyp = squippy || squippy (segment of ope)
K-4.12.1 squippyp = {4} || trip        (segment of ope)
K-4.12.2 squippyp = line || cube       (segment of ope)

K-4.13   digytpuf =  trip || refl ortho trip (gyrated ope)
```
0.879465
```K-4.14   squaf = {4} || squap     (wedge of oct || cube)
K-4.14.1 squaf = {4} || gyro cube (wedge of oct || cube)

K-4.15   octacube = oct || cube

K-4.16   squippy || gyro cube

K-4.17   squappy = {4} || gyro squippy
K-4.17.1 squappy = pt || squap
```
0.866025
```K-4.18   tisdip = trip || trip (uniform)
K-4.18.1 tisdip = {4} || cube  (uniform)
```
0.962692
```K-4.19   squappip = squap || squap    (uniform)
K-4.19.1 squappip = cube || gyro cube (uniform)
```
1
```K-4.20   tes = cube || cube     (regular)

K-4.21   cubaike =  cube || ike

K-4.22   paf =  {5} || pap
K-4.22.1 paf =  {5} || gyro pip

K-4.23   tetaco = tet || co       (segment of spid)

K-4.24   tet || tricu             (luna of spid)

K-4.25   tricuf =  {3} || tricu    (luna of spid)
K-4.25.1 tricuf =  {6} || trip     (luna of spid)

K-4.26   cubpy =  {4} || squippy   (segment of ico)
K-4.26.1 cubpy =  pt || cube       (segment of ico)

K-4.27   {3} || gyro tricu        (luna of ico)
K-4.27.1 {6} || oct               (luna of ico)

K-4.28   bidoctaco = {4} || co       (wedge of ico)

K-4.29   octaco =  oct || co       (segment of ico)

K-4.30   octatricu =  oct || tricu (luna of ico)

K-4.31   squippiaco =  squippy || co

K-4.32   squippiatricu =  squippy || tricu

K-4.33   {3} || teddi
```
1.028076
```K-4.34   trapedip = {5} || pip (uniform)
```
1.031784
```K-4.35   cubaco = cube || co
```
1.074481
```K-4.36   ipe = ike || ike             (uniform)

K-4.37   gyepippip = gyepip || gyepip

K-4.38   peppyp = peppy || peppy
K-4.38.1 peppyp = line || pip

K-4.39   pappip = pap || pap
K-4.39.1 pappip = pip || gyro pip

K-4.40   mibdip = mibdi || mibdi

K-4.41   teddipe = teddi || teddi
```
1.106168
```K-4.42   squipdip = pip || pip (uniform)
```
1.118034
```K-4.43   cope = co || co          (uniform)

K-4.44   tobcupe = tobcu || tobcu

K-4.45   tricupe = tricu || tricu
K-4.45.1 tricupe = trip || hip
```
1.130454
```K-4.46   haf = {6} || hap
K-4.46.1 haf = {6} || gyro hip
```
1.154701
```K-4.47   thiddip = {6} || hip (uniform)
```
1.183216
```K-4.48   coatut = co || tut

K-4.49   tobcuatut = tobcu || tut

K-4.50   tricuatut = tricu || tut

K-4.51   tripuf = {6} || tricu
K-4.51.1 tripuf = {3} || hip

K-4.52   octatut = oct || tut
```
1.197085
```K-4.53   happip = hap || hap      (uniform)
K-4.53.1 happip = hip || gyro hip (uniform)
```
1.224745
```K-4.54   shiddip = hip || hip  (uniform)

K-4.55   tuta = tut || inv tut (segment of rit)

K-4.56   tetatut = tet || tut  (segment of rit)
```
1.274755
```K-4.57   tuttip = tut || tut (uniform)
```
1.409438
```K-4.58   oaf = {8} || oap
K-4.58.1 oaf = {8} || gyro op
```
1.428440
```K-4.59   todip = {8} || op (uniform)
```
1.433724
```K-4.60   sniccup = snic || snic (uniform)
```
1.447009
```K-4.61   coasirco = co || sirco

K-4.62   coaescu = co || escu

K-4.63   coaop = co || op

K-4.64   {4} || gyro squacu
K-4.64.1 {8} || squap
```
1.463603
```K-4.65   oappip = oap || oap    (uniform)
K-4.65.1 oappip = op || gyro op (uniform)
```
1.48563
```K-4.66   sircope = sirco || sirco  (uniform)

K-4.67   esquigybcupe = esquigybcu || esquigybcu

K-4.68   escupe = escu || escu

K-4.69   squacupe = squacu || squacu
K-4.69.1 squacupe = cube || op

K-4.70   sodip = op || op          (uniform)

K-4.71   cubasirco = cube || sirco (segment of sidpith)

K-4.72   cube || esquibcu

K-4.73   squicuf = {4} || squacu   (wedge of sidpith)
K-4.73.1 squicuf = {8} || cube     (wedge of sidpith)
```
1.487792
```K-4.74   dope = doe || doe (uniform)
```
1.582890
```K-4.75   sircoatoe = sirco || toe
```
1.612452
```K-4.76   tutatoe = tut || toe (segment of prip)
```
1.618034
```K-4.77   doaid = doe || id

K-4.78   ikadoe = ike || doe        (segment of ex)

K-4.79   gyepip || doe

K-4.80   pappy = {5} || gyro peppy
K-4.80.1 pappy = pt || pap

K-4.81   papadoe = pap || doe

K-4.82   mibdiadoe = mibdi || doe

K-4.83   teddi adoe = teddi || doe

K-4.84   ikepy = pt || ike          (segment of ex)

K-4.85   gyepippy = pt || gyepip

K-4.86   peppypy = pt || peppy      (wedge of ex)
K-4.86.1 peppypy = line || perp {5} (wedge of ex)

K-4.87   mibdipy = pt || mibdi

K-4.88   teddipy = pt || teddi
```
1.658312
```K-4.89   tope = toe || toe (uniform)
```
1.693527
```K-4.90   iddip = id || id (uniform)

K-4.91   pobrope = pobro || pobro

K-4.92   perope = pero || pero
```
1.702385
```K-4.93   daf = {10} || dap
K-4.93.1 daf = {10} || gyro dip
```
1.717954
```K-4.94   tradedip = {10} || dip (uniform)
```
1.732051
```K-4.95   coatoe = co || toe (segment of rico)
```
1.747560
```K-4.96   dappip = dap || dap      (uniform)
K-4.96.1 dappip = dip || gyro dip (uniform)
```
1.765796
```K-4.97   squadedip = dip || dip (uniform)
```
1.785406
```K-4.98   toatic = toe || tic
```
1.847759
```K-4.99    ticcup = tic || tic      (uniform)

K-4.100   sircoatic = sirco || tic (segment of srit)

K-4.101   esquigybcu || tic

K-4.102   sircoagytic = sirco || gyro tic

K-4.103   escu || tic

K-4.104   escu || gyro tic

K-4.105   squipuf = {8} || squacu  (segment of srit)
K-4.105.1 squipuf = {4} || op      (segment of srit)

K-4.106   opatic = op || tic       (segment of srit)

K-4.107   octasirco = oct || sirco (segment of spic)

K-4.108   squippy || escu

K-4.109   squippy || squacu
```
2.213060
```K-4.110   sniddip = snid || snid (uniform)
```
2.288246
```K-4.111   sriddip = srid || srid    (uniform)

K-4.112   gyriddip = gyrid || gyrid

K-4.113   pabgyriddip = pabgyrid || pabgyrid

K-4.114   mabgyriddip = mabgyrid || mabgyrid

K-4.115   tagyriddip = tagyrid || tagyrid

K-4.116   diriddip = dirid || dirid

K-4.117   pecupe =  pecu || pecu
K-4.117.1 pecupe =  pip || dip

K-4.118   pagydriddip = pagydrid || pagydrid

K-4.119   magydriddip = magydrid || magydrid

K-4.120   bagydriddip = bagydrid || bagydrid

K-4.121   pabidriddip = pabidrid || pabidrid

K-4.122   mabidriddip = mabidrid || mabidrid

K-4.124   tedriddip = tedrid || tedrid
```
2.370932
```K-4.125   gircope = girco || girco (uniform)
```
2.485450
```K-4.126   sridati = srid || ti
```
2.527959
```K-4.127   tipe = ti || ti (uniform)
```
2.613126
```K-4.128   ticagirco = tic || girco (segment of proh & srico)

K-4.129   coatic = co || tic       (segment of srico)
```
3.011250
```K-4.130   tiddip = tid || tid (uniform)
```
3.077684
```K-4.131   idasrid = id || srid (segment of rox)

K-4.132   id || drid

K-4.133   {5} || gyro pecu
K-4.133.1 {10} || pap

K-4.134   id || pabidrid

K-4.135   id || mabidrid

K-4.136   id || tedrid

K-4.137   ikaid = ike || id    (segment of rox)

K-4.138   gyepip || id

K-4.139   peppia pero = peppy || pero

K-4.140   gyepipa pero = gyepip || pero

K-4.141   pippy = {5} || peppy (segment of rox)
K-4.141.1 pippy = pt || pip    (segment of rox)

K-4.142   papaid = pap || id

K-4.143   mibdi || id

K-4.144   pap || pero

K-4.145   mibdi || pero

K-4.146   {5} || pero

K-4.147   teddi aid = teddi || id

K-4.148   teddi || pero
```
3.498949
```K-4.149   toagirco = toe || girco (segment of prico)
```
3.835128
```K-4.150   griddip = grid || grid (uniform)

K-4.151   tiatid = ti || tid
```
5.236068
```K-4.152   doasrid = doe || srid (segment of sidpixhi)

K-4.153   doe || drid

K-4.154   pecuf = {5} || pecu   (wedge of sidpixhi)
K-4.154.1 pecuf = {10} || pip   (wedge of sidpixhi)

K-4.155   doe || pabidrid

K-4.156   doe || mabidrid

K-4.157   doe || tedrid
```
6.073594
```K-4.158   idati = id || ti (segment of srix)
```
6.735034
```K-4.159   sridatid = srid || tid (segment of srahi)

K-4.160   gyrid || tid

K-4.161   pabgyrid || tid

K-4.162   mabgyrid || tid

K-4.163   tagyrid || tid

K-4.164   drid || tid

K-4.165   pepuf = {10} || pecu   (segment of srahi)
K-4.165.1 pepuf = {5} || dip     (segment of srahi)

K-4.166   pagydrid || tid

K-4.167   magydrid || tid

K-4.168   bagydrid || tid

K-4.169   pabidrid || tid

K-4.170   mabidrid || tid

K-4.172   tedrid || tid
```
9.744610
```K-4.173   tidagrid = tid || grid (segment of prix)
```
...
```K-4.174   n-af = {n} || n-ap
K-4.174.1 n-af = {n} || gyro n-p
```
...
```K-4.175   3,n-dip = {n} || n-p (uniform)
```
...
```K-4.176   n-appip = n-ap || n-ap    (uniform)
K-4.176.1 n-appip = n-p || gyro n-p (uniform)
```
...
```K-4.177   4,n-dip = n-p || n-p (uniform)
```

(For degenerate segmentochora, i.e. having zero heights, cf. page "finite flat complexes".)

##### Close Relatives:
1. In 2012 two sets of closely related monostratic polytopes where found:

In fact the constraint, of the lacing edges all having unit lengths too, results in some specific shift values for the base polyhedra. As those base polyhedra on the other hand are not degenerate, this conflicts to having a common circumsphere in general: within the case of pyramids only the special value n=3 results in a true convex segmentochoron (being the hex), within the case of cupolae only the special value n=2 results in a true convex segmentochoron (being trip || refl ortho trip). Even though, the values n=3,4,5 resp. n=2,3,4,5 would well generate monostratic convex regular-faced polychora (CRFs).

The closeness even could be pushed on a bit. If one of the (equivalent) bases each, which are segmentohedra in turn, would be diminished by omitting the smaller top face, i.e. maintaining therefrom only the larger bottom face, those would re-enter the range of valid segmentochora again: {n} || gyro n-py resp. {2n} || n-cu. In fact, here the necessary shifts of the bases could be assembled at the degenerate base alone. There a non-zero shift is known to be allowed.

Without narrowing those findings, those 2 families could be de-mystified a bit by using different axes: the pyramidal case is nothing but the bipyramid of the n-antiprism, while the cupolaic case is nothing but the bistratic lace tower xxo-n-oxx oxo&#xt.

Later the author realised also the existance of their ortho counterparts:

Again those can be splitted at their now always prismatic pseudofacial equator For the pyramidal ones, the case n=2 becomes subdimensional, there representing nothing but the oct. The general case here is nothing but the n-prismatic bipyramid. For the cupolaic case N=2 clearly is full dimensional, but pairs of contained squippies become corealmic and thus unite into octs. Therefore that case happens to become nothing but ope.

2. In 2014 three close relatives to pyramids have been found, which are not orbiform just because their base is not. Those are line || bilbiro, {3} || thawro, resp. {5} || pocuro. A further such case would be line || esquidpy.

3. Besides of considering 2 parallel hyperplanes cutting out monostratic layers of larger polychora, in 2012 (and more deeply in 2013) considerations about 2 intersecting equatorial hyperplanes were done. Those clearly cut out wedges. The specific choice of those hyperplanes made up the terminus lunae. Only the CRF ones were considered. The following lunae are known so far:

4. Surely the convexity restriction could be released. Some 3D examples can be found on the page on axials.
Some 4D cases would be e.g.
• 0.618034 - gikepy = pt || gike = ox3oo5/2oo&#x
• 0.618034 - sissidpy = pt || sissid = ox5/2oo5oo&#x
• 0.618034 - stasc = line || {5/2} = xo ox5/2oo&#x
• 0.658240 - shasc = line || {7/2} = xo ox7/2oo&#x
• 0.662791 - gissidagike = gissid || gike = ox3oo5/2xo&#x
• 0.692924 - gissidagid = gissid || gid = oo3ox5/2xo&#x
• 0.726543 - gikagid = gike || gid = xo3ox5/2oo&#x
• 0.707107 - hossdap = pseudo sissid || pseudo sissid = reduced( β2β5o5/2o , by β5o5/2o )
• 0.774597 - firp = tet || pseudo 2thah = reduced( xx3/2oo3ox&#x , by x3/2o3x )
• 0.866025 - "coord-axes edge star" || cube
• 0.879465 - "thah-squares star" || cube
• 0.912871 - "coord-planes square star" || cube
• 0.951057 - sidtidap = sidtid || gyro sidtid = xo5/2ox3oo3*a&#x
• 0.951057 - gidtidap = gidtid || gyro gidtid = xo5/4ox3oo3*a&#x
• 0.951057 - ditdidap = ditdid || gyro ditdid (the blend of the latter 2)
• 1              - co retro-cuploid = co || pseudo 2oct+6{4} = reduced( ox3/2xx4oo&#x, by .x3/2.x4.o )
• 1.064815 - sissidadid = sissid || did = xo5/2ox5oo&#x
• 1.765796 - siida = siid || gyro siid = xo5/2ox3xx3*a&#x
• 2.363565 - radeda tigid = did || tigid = ox5xx5/2oo&#x
• 4.352502 - diddatigid = did || tigid = ox5xx5/2oo&#x
• ...             - n/d scalene = line || perp {n/d} = xo ox-n/d-oo&#x
• ...
5. By means of external blends at the bases multistratic stacks can be derived, right in the sense of lace towers. But in general, orbiformity thereby is lost. Only few are known, which then still are. Among those clearly are the ones which can be deduced as multistratic segments of uniform or even scaliform polytopes. But there are also rare exceptional finds beyond those, e.g.
• sidrebcu = sissid || (pseudo) did || gad = xoo5/2oxo5oox&#xt
• ...

• Convex Segmentochora – (PDF)
published as: "Convex Segmentochora", by Dr. R. Klitzing, Symmetry: Culture and Science, vol. 11, 139-181, 2000
• external link (hosted by J. McNeill)

```
----
5D
----
```

### (Just some) Convex Segmentotera   (up)

0.645497
```hix =  pt || pen        (regular)
hix =  line || perp tet (regular)
hix =  {3} || perp {3}  (regular)
```
0.707107
```tac =  pen || dual pen     (regular)

hexpy =  pt || hex         (segment of tac)

octasc =  line || perp oct (lune of tac)

squete =  {3} || perp {4}  (wedge of tac)
```
0.790569
```hin =  hex || gyro hex         (uniform)

rappy =  pt || rap             (segment of hin)

trafpy =  pt || traf           (wedge of hin
segment of rappy)

bidrappy =  pt || bidrap       (segment of hin)

trippasc =  line || perp trip  (segment of hin)

editetaf =  line || tepe       (segment of hin)

tetaf =  tet || inv tepe       (segment of hin)
tetaf =  tet || hex            (segment of hin)

ditetaf = {3} || gyro tepe    (wedge of hin)
ditetaf = pen || gyro trip    (wedge of hin)

squasquasc = {4} || squasc    (wedge of hin)

tedhin =  {4} || hex           (wedge of hin)

bidhin =  oct || hex           (wedge of hin)
bidhin =  tet || inv rap       (wedge of hin)

dihin =  pen || inv rap        (segment of hin)

triddaf =  trip || bidual trip (wedge of hin)
```
0.806226
```penp =  pen || pen        (uniform)
penp =  line || tepe      (uniform)
penp =  {4} || ortho trip (uniform)
```
0.816497
```rix =  pen || rap                    (uniform)

tepepy =  pt || tepe                 (segment of rix)

octatepe =  oct || tepe              (segment of rix)

trial triddip =  {3} || gyro triddip (segment of rix)

tedrix =  {4} || lacing-ortho ( {4} || lacing-ortho {4} )
tedrix = {4} || ortho tepe
```
0.841625
```tratet = tet || tepe               (uniform)
tratet = {3} || triddip            (uniform)
tratet = trip || lacing-ortho trip (uniform)
```
0.866025
```hexip = hex || hex                      (uniform)

octpyp = line || ope                    (segment of hexip)
octpyp = octpy || octpy                 (segment of hexip)

squascop = {4} || part. ortho cube      (segment of hexip)
squascop = squasc || squasc             (segment of hexip)

dot = rap || inv rap                    (uniform)

triddippy = pt || triddip               (segment of dot)

tetcubedaw = {2}-ap || axis-ortho {4}-p (lune of dot)

teta ope = tet || ope                   (segment of dot)
teta ope = oct || rap                   (segment of dot)

taope = {3} || ope                      (wedge of dot)

tridafup = triddip || bidual triddip    (segment of dot)
```
0.895420
```squiddaf = {4}-prism || bidual {4}-prism (scaliform)

cubaope = cube || ope
```
0.912871
```troct = oct || ope              (uniform)
troct = triddip || gyro triddip (uniform)

tisquippy = {3} || tisdip       (segment of troct)
tisquippy = trip || triddip     (segment of troct)
```
0.921954
```rappip =  rap || rap          (uniform)
rappip =  ope || tepe         (uniform)

traffip = trip || inv tisdip (segment of rappip)

tepacube = tepe || cube      (wedge of rappip)
```
0.935414
```squatet =  tepe || tepe              (uniform)
squatet =  {4} || tisdip             (uniform)
squatet =  cube || lacing-ortho cube (uniform)
```
0.957427
```tratrip =  trip || tisdip     (uniform)
tratrip =  triddip || triddip (uniform)
```
1
```squoct =  ope || ope                         (uniform)
squoct =  tisdip || {3}-gyro tisdip          (uniform)

squasquippy =  {4} || tes                    (segment of squoct)

cubasquasc =  cube || squasc                 (segment of traltisdip)

traltisdip =  {3} || gyro tisdip

tisdipah =  tisdip || {6}

hexaico =  hex || ico                        (segment of rat)

rapaspid =  rap || spid                      (segment of rat)

opepy =  pt || ope                           (segment of rat)

squippyippy = pt || squippyp                (segment of rat)
squippyippy = line || cubpy                 (segment of rat)

hexaco =  hex || co                          (lune of rat)

rapaco =  rap || co                          (lune of rat)

octpy || octaco                             (lune of rat)

opeaco =  ope || co                          (segment of rat)

opeah = ope || {6}                          (wedge of rat)

tripgytricudaw = trip || ortho-gyro tricu   (wedge of rat)

penatrip =  pen || trip                      (wedge of scad)

penaspid =  pen || spid                      (segment of scad)

tepaco = tepe || co                         (lune of scad)

pexhix = trip || axis-ortho base-para tricu (wedge of scad)
```
1.040833
```tracube =  cube || tes      (uniform)
tracube =  tisdip || tisdip (uniform)
```
1.048144
```petet =  {5} || trapedip         (uniform)
petet =  pip || lacing-ortho pip (uniform)
```
1.050501
```icoap =  ico || dual ico (scaliform)

icates =  tes || ico

tessap = hex || tes

{4} || gyro tes         (wedge of tessap)
```
1.106168
```poct =  trapedip || {3}-gyro trapedip (uniform)
```
1.112583
```trike =  ike || ipe (uniform)
```
1.118034
```pent =  tes || tes        (regular)

icope =  ico || ico       (uniform)

opeacope = ope || cope   (segment of icope)

cubpyp =  line || tes     (segment of icope)

trawp = ope || hip       (wedge of icope)
trawp = traw || traw     (wedge of icope)

spiddip =  spid || spid   (uniform)

tepeacope = tepe || cope (segment of spiddip)

tricufip = hip || tisdip
tricufip = tricuf || tricuf
```
1.143215
```trapip =  pip || squipdip      (uniform)
trapip =  trapedip || trapedip (uniform)
```
1.154701
```traco =  co || cope            (uniform)

tritricu =  triddip || thiddip (segment of traco)
```
1.172604
```hatet =  {6} || thiddip          (uniform)
hatet =  hip || lacing-ortho hip (uniform)

pexhix = {6} || triddip
```
1.185120
```squike =  ipe || ipe (uniform)
```
1.190238
```opeatut = ope || tut            (wedge of spix)

copatut = cope || tut           (wedge of spix)

rapatut = rap || tut            (wedge of spix)

rapalsrip = rap || inv srip     (segment of spix)

spidasrip = spid || srip        (segment of spix)

tetacope = tet || cope          (segment of spix)

triddipa hip = {3} || tricupe   (wedge of spix)
triddipa hip = trip || tripuf   (wedge of spix)
triddipa hip = triddip || hip   (wedge of spix)

tripa thiddip = {6} || tricupe  (wedge of spix)
tripa thiddip = trip || thiddip (wedge of spix)

pabex hix = thiddip || antipara thiddip (scaliform)

triddip althiddip = triddip || gyro thiddip
```
1.213922
```pecube =  squipdip || squipdip (uniform)
```
1.224745
```octhipdaw = {3}-ap || axis-ortho {6}-p

hoct = thiddip || {3}-gyro thiddip (uniform)

hisquippy = {6} || shiddip         (segment of hoct)

squaco = cope || cope              (uniform)

squatricu = tisdip || shiddip      (segment of squaco)
squatricu = tricupe || tricupe     (segment of squaco)

icarit = ico || rit            (segment of nit)

octco tuttric = octaco || tut  (wedge of nit)
octco tuttric = oct || coatut  (wedge of nit)
octco tuttric = co || octatut  (wedge of nit)

rapasrip = rap || srip         (segment of nit)

pabdinit = srip || inv srip    (scaliform,
segment of nit)

octacope = oct || cope         (segment of nit)

trial tricupe = {3} || tricupe (wedge of nit)

tisdippy = pt || tisdip        (segment of nit)

ica tutcup = ico || tuta       (segment of nit)

coa tutcup = co || tuta        (wedge of nit)

coarit = co || rit             (wedge of nit)
```
1.227160
```tessarit  = tes || rit
```
1.258306
```trahip  = thiddip || thiddip (uniform)
trahip  = hip || shiddip     (uniform)
```
1.274755
```tepatut = tepe || tut         (wedge of siphin)

tutaf = tut || inv tuttip     (wedge of siphin)

tutas = tuta || alt. tuta     (scaliform,
segment of siphin)

rita = rit || gyro rit        (scaliform,
segment of siphin)

hexalrit =  hex || gyro rit    (segment of siphin)

octa tutcup = oct || tuta

tripalhip = trip || lacing-ortho hip

tetco tuttric = tet || coatut (segment of penasrip)
tetco tuttric = co || tetatut (segment of penasrip)
tetco tuttric = tut || tetaco (segment of penasrip)

penasrip = pen || srip

spidatip = spid || tip

sripaltip = srip || inv tip
```
1.284523
```srippip =  srip || srip        (uniform)

opeatuttip = ope || tuttip    (segment of srippip)

copea tuttip = cope || tuttip (segment of srippip)

tripufip =  trip || shiddip    (wedge of srippip)
tripufip = tripuf || tripuf   (wedge of srippip)
```
1.290994
```rapatip = rap || tip        (segment of sarx)

sripatip = srip || tip      (segment of sarx)

coatuttip = co || tuttip    (segment of sarx)

trathiddip = {3} || thiddip (segment of sarx)
```
1.302772
```pepip =  pedip || pedip (uniform)
```
1.307032
```tratut =  tut || tuttip (uniform)
```
1.322876
```hacube =  shiddip || shiddip      (uniform)

rittip =  rit || rit              (uniform)

tutcupip = tuttip || inv tuttip  (segment of rittip)
tutcupip = tuta || tuta          (segment of rittip)

tepeatuttip =  tepe || tuttip     (segment of rittip)
tepeatuttip =  tetatut || tetatut (segment of rittip)
```
1.360147
```tippip =  tip || tip (uniform)
```
1.369306
```squatut =  tuttip || tuttip (uniform)
```
1.414214
```pennatip = pen || tip       (segment of rin)

tipadeca =  tip || deca      (segment of rin)

octatuttip = oct || tuttip  (segment of sibrid)

sripadeca = srip || deca    (half of sibrid)

hatricu = thiddip || hiddip (half of haco)
```
1.442951
```otet =  {8} || todip          (uniform)
otet =  op || lacing-ortho op (uniform)
```
1.462497
```trasnic =  snic || sniccup (uniform)
```
1.485633
```owoct =  todip || {3}-gyro todip (uniform)
```
1.5
```decap =  deca || deca (uniform)
```
1.502958
```rita sidpith =  rit || sidpith
```
1.513420
```trasirco =  sirco || sircope (uniform)
```
1.515539
```tradoe =  doe || dope (uniform)
```
1.518409
```squasnic =  sniccup || sniccup (uniform)
```
1.567516
```ocube =  sodip || sodip         (uniform)

squasirco =  sircope || sircope (uniform)

sidpithip =  sidpith || sidpith (uniform)

squicuffip = squicuf || squicuf (wedge of sidpithip)
squicuffip = tes || op          (wedge of sidpithip)
```
1.569562
```squadoe =  dope || dope (uniform)
```
1.620185
```ritag thex = rit || gyro thex (segment of sirhin)

thexa = thex || gyro thex     (scaliform,
segment of sirhin)

teta tuttip = tet || tuttip   (segment of sirhin)

rapadeca = rap || deca        (segment of sirhin)

deca aprip = deca || prip     (segment of sirhin)

tutcupa toe = tuta || toe     (wedge of sirhin)
```
1.632993
```tipalprip = tip || inv prip (segment of cappix)

tuttipa toe = tuttip || toe (wedge of cappix)
```
1.658312
```triddippa hiddip = trddip || hiddip (segment of card)

pripa = prip || inv prip            (segment of card)

sripaprip = srip || prip            (segment of card)

thexip =  thex || thex               (uniform)
```
1.683251
```tratoe =  toe || tope (uniform)
```
1.688194
```prippip =  prip || prip            (uniform)

tuttipa tope = tuttip || tope     (segment of prippip)
tuttipa tope = tutatoe || tutatoe (segment of prippip)
```
1.693527
```exip =  ex || ex      (uniform)

gappip =  gap || gap  (uniform)

```
1.717954
```trid =  id || iddip (uniform)
```
1.732051
```squatoe =  tope || tope        (uniform)

icathex = ico || thex         (segment of sart)

rico || thex                  (segment of sart)

sripalprip = srip || inv prip (segment of sart)

trashiddip = {3} || shiddip   (segment of sart)

cotut totric = co || tutatoe  (wedge of sart)
cotut totric = coatut || toe  (wedge of sart)
cotut totric = tut || coatoe  (wedge of sart)
```
1.738546
```rico || sadi
```
1.765796
```squid =  iddip || iddip (uniform)
```
1.778824
```ricoa =  rico || gyro rico (scaliform)
```
1.802776
```ricope =  rico || rico       (uniform)

copatope = cope || tope     (segment of ricope)
copatope = coatoe || coatoe (segment of ricope)
```
1.847759
```ica sidpith =  ico || sidpith

ricasrit =  rico || srit

ricoaspic =  rico || spic
```
1.848423
```pripalgrip =  prip || gyro grip (segment of pattix)

tutatope =  tut || tope         (segment of pattix)
```
1.870173
```tratic =  tic || ticcup (uniform)
```
1.870829
```ritarico =  rit || rico   (segment of spat)

spidaprip =  spid || prip (segment of spat)

pripagrip =  prip || grip (segment of spat)

gripa = grip || inv grip (segment of spat)

copatoe =  cope || toe    (wedge of spat)
```
1.910497
```grippip =  grip || grip (uniform)
```
1.914214
```squatic =  ticcup || ticcup (uniform)

spiccup =  spic || spic     (uniform)

srittip =  srit || srit     (segment of span)

sidpith || srit            (segment of span)
```
1.914854
```deca agrip = deca || grip (segment of pirx)
```
1.994779
```ofx3xoo4ooo&#xt || o3o4x
```
2.117085
```twacube =  sitwadip || sitwadip (uniform)
```
2.150581
```taha = tah || gyro tah (scaliform,
wedge of hejak)

hinarin = hin || rin   (segment of hejak)

tipagrip = tip || grip
```
2.179449
```tahp =  tah || tah (uniform)
```
2.207107
```tattip =  tat || tat (uniform)

srit || tat         (segment of sirn)

rap || tip          (segment of sirn)

sirco || ticcup     (segment of sirn)

{4} || todip        (segment of sirn)
```
2.231808
```trasnid =  snid || sniddip (uniform)
```
2.236068
```ricatah = rico || tah    (segment of sibrant)

sripagrip = srip || grip (segment of sibrant)

coatope = co || tope     (wedge of sibrant)
```
2.268840
```squasnid =  sniddip || sniddip (uniform)
```
2.291288
```gippiddip =  gippid || gippid (uniform)
```
2.306383
```trasrid =  srid || sriddip (uniform)
```
2.327373
```gripagippid = grip || gippid (segment of cograx)
```
2.342236
```squasrid =  sriddip || sriddip (uniform)
```
2.371708
```thexagtah =  thex || gyro tah
```
2.388442
```tragirco =  girco || gircope (uniform)
```
2.423081
```squagirco =  gircope || gircope (uniform)

prittip =  prit || prit         (uniform)
```
2.544388
```trati =  ti || tipe (uniform)
```
2.576932
```squati =  tipe || tipe (uniform)
```
2.632865
```ritasrit =  rita || srit

sricoa =  srico || gyro srico (scaliform)
```
2.647378
```tico || prissi
```
2.660531
```prohp =  proh || proh     (uniform,
segment of carnit)

prit || proh             (segment of carnit)

prit || srit             (segment of carnit)

hodip || tisdip          (segment of carnit)

sricope =  srico || srico (uniform)
```
2.692582
```ticope =  tico || tico (uniform)
```
2.738613
```pripa gippid = prip || gippid (segment of pattit)
```
2.878460
```proh || tat (segment of capt)
```
3
```tahatico = tah || tico (segment of pirt)
```
3.025056
```tratid =  tid || tiddip (uniform)
```
3.047217
```grittip =  grit || grit (segment of prin)
```
3.052479
```squatid =  tiddip || tiddip (uniform)
```
3.118034
```roxip =  rox || rox (uniform)
```
3.239235
```prohagrit = proh || grit  (segment of pattin)
```
3.450631
```contip =  cont || cont (uniform)
```
3.522336
```pricoa =  prico || gyro prico (scaliform)
```
3.534493
```pricope =  prico || prico        (uniform)

gidpithip =  gidpith || gidpith (uniform,
segment of cogart)
```
3.736068
```hipe =  hi || hi (uniform)
```
3.845977
```tragrid =  grid || griddip (uniform)
```
3.867584
```squagrid =  griddip || griddip (uniform)
```
3.988340
```gritta gidpith = grit || gidpith (segment of cogrin)
```
4.311477
```gricoa =  grico || gyro grico (scaliform)
```
4.328427
```gricope =  grico || grico (uniform)
```
4.562051
```rahipe =  rahi || rahi (uniform)
```
4.670365
```thipe =  thi || thi (uniform)
```
4.749980
```texip =  tex || tex (uniform)
```
4.776223
```grixip =  grix || grix (uniform)
```
5.194028
```gippiccup =  gippic || gippic (uniform)
```
5.259887
```sidpixhip =  sidpixhi || sidpixhi (uniform)
```
6.094140
```srixip =  srix || srix (uniform)
```
6.753568
```srahip =  srahi || srahi (uniform)
```
7.596108
```xhip =  xhi || xhi (uniform)
```
8.294035
```prahip =  prahi || prahi (uniform)
```
9.757429
```prixip =  prix || prix (uniform)
```
11.263210
```grahip =  grahi || grahi (uniform)
```
12.796423
```gidpixhip =  gidpixhi || gidpixhi (uniform)
```
...
```3,n-dippip =  n-p || 4,n-dip     (uniform)
3,n-dippip =  3,n-dip || 3,n-dip (uniform)
```
...
```n,cube-dip =  4,n-dip || 4,n-dip (uniform)
```
...
```n,m-dippip =  n,m-dip || n,m-dip (uniform)
```
...
```n,m-dafup =  n,m-dip || bidual n,m-dip (scaliform)
```

(For degenerate segmentotera, i.e. having zero heights, cf. page "finite flat complexes".)

Some non-convex segmentotera would be:

• 0.623054 - stadow = pentagram || fully perp. pentagram (aka: star disphenoid)
• 0.636010 - sissidisc = line || fully perp. sissid (aka: sissid scalene)
• 0.674163 - shadow = small heptagram || fully perp. small heptagram (aka: small heptagrammic disphenoid)
• 0.680827 - gashia = gashi || dual gashi (aka: gashi antiprism)
• 1.074481 - sishiap = narrower sishi || sishi
• 1.248606 - ragashia = ragashi || inv ragashi (aka: ragashi alterprism)
• 1.618034 - sirgashia = sirgashi || inv sirgashi (aka: sirgashi alterprism)
• 1.693527 - gohip = gohi || gohi
• 1.917564 - righia = righi || inv righi (aka: righi alterprism)
• 2.321762 - sidtaxhiap = sidtaxhi || alt. sidtaxhi (aka: sidtaxhi alterprism, uniform)
• 3.404434 - sirghia = sirghi || inv sirghi (aka: sirghi alterprism)
• 3.855219 - stut phiddixa = stut phiddix || alt. stut phiddix (aka: stut phiddix alterprism)
• 4.923348 - pirghia = pirghi || inv pirghi (aka: pirghi alterprism)
• 5.345177 - wavhiddixa = wavhiddix || alt. wavhiddix (aka: wavhiddix alterprism)
• 6.893126 - sphiddixa = sphiddix || alt. sphiddix (aka: sphiddix alterprism)

```
----
6D
----
```

### (Just some) Convex Segmentopeta   (up)

0.654654
```hop =  pt || hix        (regular)
hop =  line || perp pen (regular)
hop =  {3} || perp tet  (regular)
```
0.707107
```gee =  hix || inv hix      (regular)

tacpy =  pt || tac         (segment of gee)

hexasc =  line || perp hex (lune of gee)

octete =  {3} || perp oct  (wedge of gee)

squepe =  {4} || perp tet  (wedge of gee)
```
0.816497
```hixip =  hix || hix               (uniform)
hixip =  line || penp             (uniform)
hixip =  trip || part. ortho trip (uniform)

dijak = hin || tac          (segment of jak)

tedjak =  hex || hin         (scaliform,
tridiminished jak)

hedjak = {4} || hin         (wedge of jak)

hinpy =  pt || hin           (segment of jak)

rapesc =  line || perp rap   (segment of jak)

tripal triddip = trip || dual-perp triddip
(wedge of jak)

hixalrix =  hix || inv rix   (segment of jak)

penaf =  pen || inv penp     (segment of jak)

rapalpenp =  rap || inv penp (segment of jak)

trippete = {3} || perp trip (segment of jak)
```
0.845154
```ril =  hix || rix                  (uniform)

penppy =  pt || penp               (segment of ril)

rapa penp =  rap || penp           (segment of ril)

trial tratet = {3} || dual tratet (segment of ril)

octa tratet =  oct || tratet       (segment of ril)
```
0.856349
```trapen =  pen || penp   (uniform)
trapen =  {3} || tratet (uniform)
```
0.866025
```hax =  hin || gyro hin     (uniform)

taccup =  tac || tac       (uniform)

tetdip =  tet || tratet    (uniform)

tratetdafup = tratet || bidual tratet (scaliform)

tetal tratet =  tet || inv tratet

tepasc =  line || perp tepe

rixpy =  pt || rix         (segment of hax)

hixadot =  hix || dot      (segment of hax)

hixacube =  hix || cube    (wedge of hax)

rixa = rix || inv rix     (scaliform,
segment of hax)

hexaf =  hex || gyro hexip (segment of hax)
```
0.912871
```trahex =  hex || hexip (uniform)
```
0.925820
```bril =  rix || dot                     (uniform)

tratetpy =  pt || tratet               (segment of bril)

tratet altroct =  tratet || gyro troct (segment of bril)

tet || troct                          (segment of bril)

pena rappip =  pen || rappip           (segment of bril)
```
0.935414
```hinnip =  hin || hin (uniform)

tetafip = tepe || inv squatet (segment of hinnip)
tetafip = tepe || hexip       (segment of hinnip)
```
0.948683
```squapen =  penp || penp   (uniform)
squapen =  {4} || squatet (uniform)
```
0.957427
```rixip =  rix || rix         (uniform)

tepepyp = line || squatet  (segment of rixip)
tepepyp = tepepy || tepepy (segment of rixip)
```
0.966092
```trarap = rap || rappip   (uniform)
trarap = tratet || troct (uniform)
```
1
```dotip =  dot || dot           (uniform)
dotip =  rappip || inv rappip (uniform)

squahex =  hexip || hexip     (uniform)

hexippy =  pt || hexip        (segment of rag)

hexipaico =  hexip || ico     (wedge of rag)

taccarat =  tac || rat        (segment of rag)

dotpy =  pt || dot            (segment of mo)

hinro =  hin || rat           (segment of mo)
```
1.123033
```icaf = ico || dual icope
```
1.195229
```rixalspix = rix || inv spix (segment of scal)

```
1.224745
```ax =  pent || pent        (regular)

dottaspix =  dot || spix  (segment of brag)

spixa = spix || inv spix (segment of brag)

ratanit =  rat || nit     (segment of brag)
```
1.228783
```pentanit = pent || nit
```
1.290994
```spixip =  spix || spix         (uniform)

ritgyt = rit || gyro rita     (scaliform,
wedge of rojak)

hinanit =  hin || nit          (segment of rojak)

nitasiphin =  nit || siphin    (segment of rojak)

ratasiphin =  rat || siphin    (segment of rojak)

rixaspix =  rix || spix        (segment of rojak)

spixalsarx =  spix || inv sarx (segment of rojak)
```
1.322876
```tettut =  tut || tratut (uniform)
```
1.414214
```tixip =  tix || tix           (uniform)

nitarin =  nit || rin         (segment of brox)

rixasarx =  rix || sarx       (segment of brox)

sarxasibrid =  sarx || sibrid (segment of brox)
```
1.418705
```pentarin =  pent || rin
```
1.581139
```bittixa =  bittix || inv bittix (scaliform)
```
1.614654
```open =  {8} || otet (uniform)
```
1.632993
```thexgyt =  thex || gyro thexa (scaliform,
wedge of hejak)

hinarin = hin || rin         (segment of hejak)
```
1.658312
```cappixa = cappix || alt cappix (scaliform)
```
1.732051
```cardip =  card || card        (uniform,
segment of ram)

dottasibrid = dot || sibrid  (segment of ram)

sibridacard = sibrid || card (segment of ram)

nitasirhin = nit || sirhin   (segment of ram)

sirhinasart = sirhin || sart (segment of ram)
```
2.160247
```tahgyt =  tah || gyro taha (scaliform,
wedge of harjak)

rinathin = rin || thin    (segment of harjak)
```
3
```gocadip =  gocad || gocad (uniform)
```
...
```(n,pen)-dip =  {n} || (n,tet)-dip (uniform)
```

Some non-convex segmentopeta would be:

```
----
7D
----
```

### (Just some) Convex Segmentoexa   (up)

0.661438
```oca =  pt || hop        (regular)
oca =  line || perp hix (regular)
oca =  {3} || perp pen  (regular)
oca =  tet || perp tet  (regular)
```
0.707107
```zee = hop || inv hop       (regular)

geepy = pt || gee          (segment of zee)

taccasc = line || perp tac (lune of zee)

hexete = {3} || perp hex   (wedge of zee)

squix = {4} || perp pen    (wedge of zee)

octepe = tet || perp oct   (wedge of zee)
```
0.823754
```hopip =  hop || hop (uniform)
```
0.866025
```roc =  hop || ril            (uniform)

octatetdip =  oct || tetdip  (wedge of roc)

geep =  gee || gee           (uniform)
geep =  hixip || inv hixip   (uniform)

trahix = hix || hixip       (uniform,
wedge of naq)

rila = ril || alt. ril      (scaliform,
segment of naq)

jaka = jak || alt. jak      (scaliform,
segment of naq)

trapendafup = trapen || bidual trapen (scaliform)

jakpy =  pt || jak           (segment of naq)

hixaf =  hix || inv hixip    (segment of naq)

hopalril =  hop || inv ril   (segment of naq)

gahax =  gee || hax          (segment of naq)

hinsc =  line || perp hin    (wedge of naq)

hexalhax =  hex || alt. hax  (wedge of naq)

rapete =  {3} || perp rap
```
0.935414
```hesa =  hax || gyro hax               (uniform)

rilpy =  pt || ril                    (segment of hesa)

hexal trahex =  hex || gyro trahex    (segment of hesa)

hopabril =  hop || bril               (segment of hesa)

rilalbril =  ril || alt. bril         (segment of hesa)

tetal tetdip =  tet || dual tetdip

tethex =  hex || trahex               (uniform)
tethex =  tetdip || para-dual tetdip  (uniform)
tethex =  hexip || lacing-ortho hexip (uniform)

penpasc =  line || perp penp
```
0.957427
```squahix =  hixip || hixip (uniform)

jakip =  jak || jak       (uniform)
```
0.968246
```broc =  ril || bril (uniform)
```
0.978945
```trahin =  hin || hinnip (uniform)
```
0.981981
```rillip =  ril || ril (uniform)
```
0.991632
```trippen =  trapen || trapen (uniform)
```
1
```he =  bril || inv bril       (uniform)

tetdippy =  pt || tetdip     (segment of he)

squarat = ratip || ratip    (uniform)
diminishing of barz)

tettepe =  tetdip || tetdip  (uniform)

trarix = rix || rixip       (uniform,
wedge of laq)

haxpy =  pt || hax           (segment of laq)

haxarag = hax || rag        (segment of laq)

jakamo =  jak || mo          (segment of laq)

hopalbril =  hop || inv bril (segment of laq)

brilastaf =  bril || staf    (segment of laq)

taccuppy = pt || taccup     (segment of rez)

garag =  gee || rag          (segment of rez)

rilastaf =  ril || staf      (segment of rez)

hopastaf =  hop || staf      (segment of suph
diminishing of laq)

rixasc =  line || perp rix

trial trahex =  {3} || inv trahex

trahex aico =  trahex || ico
```
1.052209
```brillip =  bril || bril (uniform)
```
1.060660
```haxip =  hax || hax (uniform)
```
1.118034
```tratratrip =  trittip || trittip (uniform)
```
1.154701
```tratac =  tac || taccup (uniform)
```
1.224745
```trahexpy =  pt || trahex  (segment of barz)

ragabrag =  rag || brag   (segment of barz)

scala = scal || inv scal (scaliform,
segment of barz)
```
1.322876
```hept = ax || ax               (regular)

brilalspil = bril || inv spil (segment of sco)

scala spil = scal || spil     (segment of sco)

haxabrag = hax || brag        (segment of lin)

rojaka = rojak || alt. rojak  (scaliform,
segment of lin)

moarojak = mo || rojak        (segment of lin)

bragasochax = brag || sochax  (segment of lin)

brilpy = pt || bril           (segment of lin)
```
1.414214
```bragabrox =  brag || brox (segment of sez)
```
1.457317
```ohix = {8} || open (uniform)
```
1.581139
```broxarax = brox || rax (segment of bersa)
```
1.732051
```haxabrox =  hax || brox        (segment of rolaq)

broxa sophax =  brox || sophax (segment of rolaq)

rojaka hejak =  rojak || hejak (segment of rolaq)
```
...
```n,n,n-tippip =  n,n,n-tip || n,n,n-tip (uniform)
```

Some non-convex segmentoexa would be:

• 0.831254 - sissiddow = sissid || fully perp. sissid (aka: sissid disphenoid)

```
----
8D
----
```

### (Just some) Convex Segmentozetta   (up)

0.666667
```ene  = pt || oca (regular)
```
0.707107
```ek  = oca || dual oca (regular)

zeepy  = pt || zee   (segment of ek)
```
0.829156
```ocpe  = oca || oca (uniform)
```
0.866025
```zeep  = zee || zee (uniform)
```
0.872872
```trihop  = hop || hopip (uniform)
```
0.881917
```rene  = oca || roc (uniform)
```
0.963624
```squahop  = hopip || hopip (uniform)
```
1
```trajak = jak || jakip        (uniform,
wedge of fy)

brene  = roc || broc          (uniform,
segment of fy)

hocto  = hesa || gyro hesa    (uniform,
segment of fy)

triphix  = trahix || trahix   (uniform)

rocpy  = pt || roc            (segment of hocto)

rocahe = roc || he           (segment of hocto)

ocabroc = oca || broc        (segment of hocto)

broca = broc || inv broc     (scaliform,
segment of hocto)

ocasuph = oca || suph        (segment of soxeb)

naqpy = pt || naq            (segment of fy)

jakaf = jak || alt. jakip    (wedge of fy)

naqalaq = naq || laq         (segment of fy)

naqpe  = naq || naq           (segment of fy)

zahesa = zee || hesa         (segment of fy)

hesa arez = hesa || rez      (segment of fy)

ocalroc  = oca || inv roc     (segment of fy)

rocalbroc  = roc || inv broc  (segment of fy)

hexal hesa  = hex || alt hesa (wedge of codify)

octa tethex  = oct || tethex

tethex aico  = tethex || ico
```
1.224745
```rezabarz =  rez || barz (segment of bark)
```
1.414214
```octo  = hept || hept     (regular)

barzasez  = barz || sez (segment of tark)

hesapy  = pt || hesa     (segment of bay)

laqalin  = laq || lin    (segment of bay)

linaranq  = lin || ranq  (segment of bay)
```

```
----
9D
----
```

### (Just some) Convex Segmentoyotta   (up)

0.670820
```day  = pt || ene (regular)
```
0.707107
```vee  = ene || dual ene (regular)
```
0.833333
```enep  = ene || ene (uniform)
```
0.866025
```ekip  = ek || ek (uniform)
```
0.894427
```reday  = ene || rene (uniform)
```
0.968246
```squoc  = ocpe || ocpe (uniform)
```
1.024695
```breday  = rene || brene (uniform)
```
1.060660
```henne  = hocto || gyro hocto (uniform)
```
1.5
```enne  = octo || octo (regular)
```

```
-----
10D
-----
```

### (Just some) Convex Segmentoxenna   (up)

```ux  = pt || day (regular)
```ka  = day || dual day (regular)
```ru  = day || reday (uniform)